From e6cbbf93146c693ed5246e4b71eee5915db5bb90 Mon Sep 17 00:00:00 2001 From: Daniel Scime Date: Wed, 1 May 2019 16:22:27 -0400 Subject: [PATCH] Beginning to add data defs from smiths to SWHS --- code/SRS/Makefile | 24 + code/SRS/SWHS_SRS.tex | 1411 +++ code/Website/SWHS_SRS.css | 93 + code/Website/SWHS_SRS.html | 10571 ++++++++++++++++++ code/drasil-example/Drasil/SWHS/DataDefs.hs | 32 +- code/drasil-example/Drasil/SWHS/IMods.hs | 10 +- code/stable/glassbr/SRS/GlassBR_SRS-blx.bib | 11 + code/stable/glassbr/SRS/GlassBR_SRS.pdf | Bin 0 -> 722026 bytes code/stable/glassbr/SRS/GlassBR_SRS.run.xml | 92 + code/stable/glassbr/SRS/bibfile.bib | 69 + code/stable/swhs/SRS/SWHS_SRS-blx.bib | 11 + code/stable/swhs/SRS/SWHS_SRS.pdf | Bin 0 -> 240122 bytes code/stable/swhs/SRS/SWHS_SRS.run.xml | 92 + code/stable/swhs/SRS/SWHS_SRS.tex | 37 +- code/stable/swhs/SRS/bibfile.bib | 63 + code/stable/swhs/SWHS_SRS.synctex(busy) | 0 16 files changed, 12502 insertions(+), 14 deletions(-) create mode 100644 code/SRS/Makefile create mode 100644 code/SRS/SWHS_SRS.tex create mode 100644 code/Website/SWHS_SRS.css create mode 100644 code/Website/SWHS_SRS.html create mode 100644 code/stable/glassbr/SRS/GlassBR_SRS-blx.bib create mode 100644 code/stable/glassbr/SRS/GlassBR_SRS.pdf create mode 100644 code/stable/glassbr/SRS/GlassBR_SRS.run.xml create mode 100644 code/stable/glassbr/SRS/bibfile.bib create mode 100644 code/stable/swhs/SRS/SWHS_SRS-blx.bib create mode 100644 code/stable/swhs/SRS/SWHS_SRS.pdf create mode 100644 code/stable/swhs/SRS/SWHS_SRS.run.xml create mode 100644 code/stable/swhs/SRS/bibfile.bib delete mode 100644 code/stable/swhs/SWHS_SRS.synctex(busy) diff --git a/code/SRS/Makefile b/code/SRS/Makefile new file mode 100644 index 0000000000..901fa9b63a --- /dev/null +++ b/code/SRS/Makefile @@ -0,0 +1,24 @@ +ifeq "$(OS)" "Windows_NT" + TARGET_EXTENSION=.exe + RM=del +else + UNAME_S := $(shell uname -s) + ifeq ($(UNAME_S), Linux) + TARGET_EXTENSION= + RM=rm + endif + ifeq ($(UNAME_S), Darwin) + TARGET_EXTENSION= + RM=rm + endif +endif + +srs: SWHS_SRS.pdf + +SWHS_SRS.pdf: SWHS_SRS.tex + lualatex $(TEXFLAGS) SWHS_SRS + -bibtex $(BIBTEXFLAGS) SWHS_SRS + lualatex $(TEXFLAGS) SWHS_SRS + lualatex $(TEXFLAGS) SWHS_SRS + +.PHONY: srs diff --git a/code/SRS/SWHS_SRS.tex b/code/SRS/SWHS_SRS.tex new file mode 100644 index 0000000000..6c07adefdb --- /dev/null +++ b/code/SRS/SWHS_SRS.tex @@ -0,0 +1,1411 @@ +\documentclass[12pt]{article} +\usepackage{fontspec} +\usepackage{fullpage} +\usepackage{hyperref} +\hypersetup{bookmarks=true,colorlinks=true,linkcolor=red,citecolor=blue,filecolor=magenta,urlcolor=cyan} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{mathtools} +\usepackage{unicode-math} +\usepackage{tabu} +\usepackage{longtable} +\usepackage{booktabs} +\usepackage{caption} +\usepackage{graphics} +\usepackage{enumitem} +\usepackage{filecontents} +\usepackage[backend=bibtex]{biblatex} +\usepackage{url} +\newlist{symbDescription}{description}{1} +\setlist[symbDescription]{noitemsep, topsep=0pt, parsep=0pt, partopsep=0pt} +\setmathfont{Latin Modern Math} +\global\tabulinesep=1mm +\bibliography{bibfile} +\title{Software Requirements Specification for Solar Water Heating Systems Incorporating PCM} +\author{Thulasi Jegatheesan, Brooks MacLachlan, and W. Spencer Smith} +\begin{document} +\maketitle +\tableofcontents +\newpage +\section{Reference Material} +\label{Sec:RefMat} +This section records information for easy reference. +\subsection{Table of Units} +\label{Sec:ToU} +The unit system used throughout is SI (Système International d'Unités). In addition to the basic units, several derived units are also used. For each unit, the table lists the symbol, a description and the SI name. +\begin{longtable*}{l l} +\toprule +Symbol & Description +\\ +\midrule +\endhead +${}^{\circ}$C & temperature (centigrade) +\\ +J & energy (joule) +\\ +kg & mass (kilogram) +\\ +m & length (metre) +\\ +s & time (second) +\\ +W & power (watt) +\\ +\bottomrule +\label{Table:ToU} +\end{longtable*} +\subsection{Table of Symbols} +\label{Sec:ToS} +The table that follows summarizes the symbols used in this document along with their units. The choice of symbols was made to be consistent with the heat transfer literature and with existing documentation for solar water heating systems. The symbols are listed in alphabetical order. +\begin{longtabu}{l X[l] l} +\toprule +Symbol & Description & Units +\\ +\midrule +\endhead +${A_{C}}$ & Heating coil surface area & $\text{m}^{2}$ +\\ +${A_{in}}$ & Surface area over which heat is transferred in & $\text{m}^{2}$ +\\ +${A_{out}}$ & Surface area over which heat is transferred out & $\text{m}^{2}$ +\\ +${A_{P}}$ & Phase change material surface area & $\text{m}^{2}$ +\\ +$C$ & Specific heat capacity & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${C^{L}}$ & Specific heat capacity of a liquid & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${C^{S}}$ & Specific heat capacity of a solid & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${C^{V}}$ & Specific heat capacity of a vapour & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${C_{W}}$ & Specific heat capacity of water & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${{C_{P}}^{L}}$ & Specific heat capacity of PCM as a liquid & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${{C_{P}}^{S}}$ & Specific heat capacity of PCM as a solid & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +$D$ & Diameter of tank & m +\\ +$E$ & Sensible heat & J +\\ +${E_{P}}$ & Change in heat energy in the PCM & J +\\ +${E_{W}}$ & Change in heat energy in the water & J +\\ +${{{E_{P}}_{melt}}^{init}}$ & Change in heat energy in the PCM at the instant when melting begins & J +\\ +$g$ & Volumetric heat generation per unit volume & $\frac{\text{W}}{\text{m}^{3}}$ +\\ +$h$ & Convective heat transfer coefficient & $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ +\\ +${h_{C}}$ & Convective heat transfer coefficient between coil and water & $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ +\\ +${H_{f}}$ & Specific latent heat of fusion & $\frac{\text{J}}{\text{kg}}$ +\\ +${h_{min}}$ & Minimum thickness of a sheet of PCM & m +\\ +${h_{P}}$ & Convective heat transfer coefficient between PCM and water & $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ +\\ +$L$ & Length of tank & m +\\ +$m$ & Mass & kg +\\ +${m_{P}}$ & Mass of phase change material & kg +\\ +${m_{W}}$ & Mass of water & kg +\\ +$\mathbf{\hat{n}}$ & Unit outward normal vector for a surface & -- +\\ +$Q$ & Latent heat & J +\\ +$q$ & Heat flux & $\frac{\text{W}}{\text{m}^{2}}$ +\\ +${q_{C}}$ & Heat flux into the water from the coil & $\frac{\text{W}}{\text{m}^{2}}$ +\\ +${q_{in}}$ & Heat flux input & $\frac{\text{W}}{\text{m}^{2}}$ +\\ +${q_{out}}$ & Heat flux output & $\frac{\text{W}}{\text{m}^{2}}$ +\\ +${q_{P}}$ & Heat flux into the PCM from water & $\frac{\text{W}}{\text{m}^{2}}$ +\\ +${Q_{P}}$ & Latent heat energy added to PCM & J +\\ +$\mathbf{q}$ & Thermal flux vector & $\frac{\text{W}}{\text{m}^{2}}$ +\\ +$S$ & Surface & $\text{m}^{2}$ +\\ +$T$ & Temperature & ${}^{\circ}$C +\\ +$t$ & Time & s +\\ +$ΔT$ & Change in temperature & ${}^{\circ}$C +\\ +${T_{boil}}$ & Boiling point temperature & ${}^{\circ}$C +\\ +${T_{C}}$ & Temperature of the heating coil & ${}^{\circ}$C +\\ +${T_{env}}$ & Temperature of the environment & ${}^{\circ}$C +\\ +${t_{final}}$ & Final time & s +\\ +${T_{init}}$ & Initial temperature & ${}^{\circ}$C +\\ +${T_{melt}}$ & Melting point temperature & ${}^{\circ}$C +\\ +${T_{P}}$ & Temperature of the phase change material & ${}^{\circ}$C +\\ +${T_{W}}$ & Temperature of the water & ${}^{\circ}$C +\\ +${{t_{melt}}^{final}}$ & Time at which melting of PCM ends & s +\\ +${{t_{melt}}^{init}}$ & Time at which melting of PCM begins & s +\\ +${{T_{melt}}^{P}}$ & Melting point temperature for PCM & ${}^{\circ}$C +\\ +$V$ & Volume & $\text{m}^{3}$ +\\ +${V_{P}}$ & Volume of PCM & $\text{m}^{3}$ +\\ +${V_{tank}}$ & Volume of the cylindrical tank & $\text{m}^{3}$ +\\ +${V_{W}}$ & Volume of water & $\text{m}^{3}$ +\\ +$η$ & ODE parameter & -- +\\ +$ρ$ & Density & $\frac{\text{kg}}{\text{m}^{3}}$ +\\ +${ρ_{P}}$ & Density of PCM & $\frac{\text{kg}}{\text{m}^{3}}$ +\\ +${ρ_{W}}$ & Density of water & $\frac{\text{kg}}{\text{m}^{3}}$ +\\ +$τ$ & Dummy variable for integration over time & s +\\ +${τ_{W}}$ & ODE parameter for water & s +\\ +${{τ_{P}}^{L}}$ & ODE parameter for liquid PCM & s +\\ +${{τ_{P}}^{S}}$ & ODE parameter for solid PCM & s +\\ +$ϕ$ & Melt fraction & -- +\\ +$∇$ & Gradient & -- +\\ +\bottomrule +\label{Table:ToS} +\end{longtabu} +\subsection{Abbreviations and Acronyms} +\label{Sec:TAbbAcc} +\begin{longtable*}{l l} +\toprule +Abbreviation & Full Form +\\ +\midrule +\endhead +A & Assumption +\\ +DD & Data Definition +\\ +GD & General Definition +\\ +GS & Goal Statement +\\ +IM & Instance Model +\\ +LC & Likely Change +\\ +ODE & Ordinary Differential Equation +\\ +PCM & Phase Change Material +\\ +PS & Physical System Description +\\ +R & Requirement +\\ +RHS & Right Hand Side +\\ +SRS & Software Requirements Specification +\\ +SWHS & Solar Water Heating System +\\ +T & Theoretical Model +\\ +UC & Unlikely Change +\\ +Uncert. & Typical Uncertainty +\\ +\bottomrule +\label{Table:TAbbAcc} +\end{longtable*} +\section{Introduction} +\label{Sec:Intro} +Due to increasing cost, diminishing availability, and negative environmental impact of fossil fuels, there is a higher demand for renewable energy sources and energy storage technology. Solar water heating systems incorporating phase change material (PCM) use renewable energy sources and provide a novel way of storing energy. Solar water heating systems incorporating PCM improve over the traditional solar water heating systems because of their smaller size. The smaller size is possible because of the ability of PCM to store thermal energy as latent heat, which allows higher thermal energy storage capacity per unit weight. +The following section provides an overview of the Software Requirements Specification (SRS) for solar water heating systems incorporating PCM. The developed program will be referred to as Solar Water Heating System (SWHS). This section explains the purpose of this document, the scope of the system, the characteristics of the intended reader, and the organization of the document. +\subsection{Purpose of Document} +\label{Sec:DocPurpose} +The main purpose of this document is to describe the modelling of solar water heating systems incorporating PCM. The goal statements and theoretical models used in the SWHS code are provided, with an emphasis on explicitly identifying assumptions and unambiguous definitions. This document is intended to be used as a reference to provide ad hoc access to all information necessary to understand and verify the model. The SRS is abstract because the contents say what problem is being solved, but do not say how to solve it. +This document will be used as a starting point for subsequent development phases, including writing the design specification and the software verification and validation plan. The design document will show how the requirements are to be realized, including decisions on the numerical algorithms and programming environment. The verification and validation plan will show the steps that will be used to increase confidence in the software documentation and the implementation. Although the SRS fits in a series of documents that follow the so-called waterfall model, the actual development process is not constrained in any way. Even when the waterfall model is not followed, as Parnas and Clements point out \cite{parnasClements1986}, the most logical way to present the documentation is still to ``fake'' a rational design process. +\subsection{Scope of Requirements} +\label{Sec:ReqsScope} +The scope of the requirements includes thermal analysis of a single solar water heating tank incorporating PCM. Given the appropriate inputs, SWHS predicts the temperature and thermal energy histories for the water and the PCM. This entire document is written assuming that the substances inside the solar water heating tank are water and PCM. +\subsection{Characteristics of Intended Reader} +\label{Sec:ReaderChars} +Reviewers of this documentation should have an understanding of heat transfer theory from level 3 or 4 mechanical engineering and differential equations from level 1 and 2 calculus. The users of SWHS can have a lower level of expertise, as explained in \hyperref[Sec:UserChars]{Section: User Characteristics}. +\subsection{Organization of Document} +\label{Sec:DocOrg} +The organization of this document follows the template for an SRS for scientific computing software proposed by \cite{dParnas1972} and \cite{parnasClements1984}. The presentation follows the standard pattern of presenting goals, theories, definitions, and assumptions. For readers that would like a more bottom up approach, they can start reading the instance models in \hyperref[Sec:IMs]{Section: Instance Models} and trace back to find any additional information they require. +The goal statements (\hyperref[Sec:GoalStmt]{Section: Goal Statements}) are refined to the theoretical models, and the theoretical models (\hyperref[Sec:TMs]{Section: Theoretical Models}) to the instance models (\hyperref[Sec:IMs]{Section: Instance Models}). The instance models to be solved are referred to as \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}, \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}, \hyperref[IM:heatEInWtr]{IM: heatEInWtr}, and \hyperref[IM:heatEInPCM]{IM: heatEInPCM}. The instance models provide the Ordinary Differential Equation (ODEs) and algebraic equations that model the solar water heating systems incorporating PCM. SWHS solves these ODEs. +\section{General System Description} +\label{Sec:GenSysDesc} +This section provides general information about the system. It identifies the interfaces between the system and its environment, describes the user characteristics, and lists the system constraints. +\subsection{System Context} +\label{Sec:SysContext} +\hyperref[Figure:SysCon]{Fig:SysCon} shows the system context. A circle represents an external entity outside the software, the user in this case. A rectangle represents the software system itself (SWHS). Arrows are used to show the data flow between the system and its environment. +\begin{figure} +\begin{center} +\includegraphics[width=\textwidth]{../../../datafiles/SWHS/SystemContextFigure.png} +\caption{\hyperref[Figure:SysCon]{Fig:SysCon}: System Context} +\label{Figure:SysCon} +\end{center} +\end{figure} +SWHS is mostly self-contained. The only external interaction is through the user interface. The responsibilities of the user and the system are as follows: +\begin{itemize} +\item{User Responsibilities:} +\begin{itemize} +\item{Provide the input data to the system, ensuring no errors in the data entry} +\item{Take care that consistent units are used for input variables} +\end{itemize} +\item{SWHS Responsibilities:} +\begin{itemize} +\item{Detect data type mismatch, such as a string of characters instead of a floating point number} +\item{Determine if the inputs satisfy the required physical and software constraints} +\item{Calculate the required outputs} +\end{itemize} +\end{itemize} +\subsection{User Characteristics} +\label{Sec:UserChars} +The end user of SWHS should have an understanding of undergraduate Level 1 Calculus and Physics. +\subsection{System Constraints} +\label{Sec:SysConstraints} +There are no system constraints. +\section{Specific System Description} +\label{Sec:SpecSystDesc} +This section first presents the problem description, which gives a high-level view of the problem to be solved. This is followed by the solution characteristics specification, which presents the assumptions, theories, and definitions that are used. +\subsection{Problem Description} +\label{Sec:ProbDesc} +SWHS is a computer program developed to investigate the effect of employing PCM within a solar water heating tank. +\subsubsection{Terminology and Definitions} +\label{Sec:TermDefs} +This subsection provides a list of terms that are used in the subsequent sections and their meaning, with the purpose of reducing ambiguity and making it easier to correctly understand the requirements. +\begin{itemize} +\item{Heat flux: The rate of thermal energy transfer through a given surface per unit time.} +\item{Phase change material: A substance that uses phase changes (such as melting) to absorb or release large amounts of heat at a constant temperature.} +\item{Specific heat capacity: The amount of energy required to raise the temperature of the unit mass of a given substance by a given amount.} +\item{Thermal conduction: The transfer of heat energy through a substance.} +\item{Transient: Changing with time.} +\end{itemize} +\subsubsection{Physical System Description} +\label{Sec:PhysSyst} +The physical system of SWHS, as shown in \hyperref[Figure:Tank]{Fig:Tank}, includes the following elements: +\begin{itemize} +\item[PS1:]Tank containing water. +\item[PS2:]Heating coil at bottom of tank. (${q_{C}}$ represents the heat flux into the water from the coil.) +\item[PS3:]PCM suspended in tank. (${q_{P}}$ represents the heat flux into the PCM from water.) +\end{itemize} +\begin{figure} +\begin{center} +\includegraphics[width=\textwidth]{../../../datafiles/SWHS/Tank.png} +\caption{Solar water heating tank, with heat flux into the water from the coil of ${q_{C}}$ and heat flux into the PCM from water of ${q_{P}}$} +\label{Figure:Tank} +\end{center} +\end{figure} +\subsubsection{Goal Statements} +\label{Sec:GoalStmt} +Given the temperature of the heating coil, initial conditions for the temperature of the water and the temperature of the phase change material, and material properties, the goal statements are: +\begin{itemize} +\item[GS1:]Predict the temperature of the water over time. +\item[GS2:]Predict the temperature of the phase change material over time. +\item[GS3:]Predict the change in heat energy in the water over time. +\item[GS4:]Predict the change in heat energy in the PCM over time. +\end{itemize} +\subsection{Solution Characteristics Specification} +\label{Sec:SolCharSpec} +The instance models that govern SWHS are presented in \hyperref[Sec:IMs]{Section: Instance Models}. The information to understand the meaning of the instance models and their derivation is also presented, so that the instance models can be verified. +\subsubsection{Assumptions} +\label{Sec:Assumps} +This section simplifies the original problem and helps in developing the theoretical model by filling in the missing information for the physical system. The numbers given in the square brackets refer to the Theoretical Models \hyperref[Sec:TMs]{Section: Theoretical Models}, General Definitions \hyperref[Sec:GDs]{Section: General Definitions}, Data Definitions \hyperref[Sec:DDs]{Section: Data Definitions}, Instance Models \hyperref[Sec:IMs]{Section: Instance Models}, Likely Changes \hyperref[Sec:LCs]{Section: Likely Changes}, or Unlikely Changes \hyperref[Sec:UCs]{Section: Unlikely Changes}, in which the respective assumption is used. +\begin{itemize} +\item[Thermal-Energy-Only:\phantomsection\label{assumpTEO}]The only form of energy that is relevant for this problem is thermal energy. All other forms of energy, such as mechanical energy, are assumed to be negligible. \hyperref[TM:consThermE]{TM: consThermE}. +\item[Heat-Transfer-Coeffs-Constant:\phantomsection\label{assumpHTCC}]All heat transfer coefficients are constant over time. \hyperref[GD:nwtnCooling]{GD: nwtnCooling}. +\item[Constant-Water-Temp-Across-Tank:\phantomsection\label{assumpCWTAT}]The water in the tank is fully mixed, so the temperature of the water is the same throughout the entire tank. \hyperref[GD:rocTempSimp]{GD: rocTempSimp} \hyperref[DD:ht.flux.P]{DD: ht\_flux\_P}. +\item[Temp-PCM-Constant-Across-Volume:\phantomsection\label{assumpTPCAV}]The temperature of the phase change material is the same throughout the volume of PCM. \hyperref[GD:rocTempSimp]{GD: rocTempSimp} \hyperref[likeChgUTP]{LC: Uniform-Temperature-PCM} \hyperref[DD:ht.flux.P]{DD: ht\_flux\_P}. +\item[Density-Water-PCM-Constant-over-Volume:\phantomsection\label{assumpDWPCoV}]The density of water and density of PCM have no spatial variation; that is, they are each constant over their entire volume. \hyperref[GD:rocTempSimp]{GD: rocTempSimp}. +\item[Specific-Heat-Energy-Constant-over-Volume:\phantomsection\label{assumpSHECov}]The specific heat capacity of water, specific heat capacity of PCM as a solid, and specific heat capacity of PCM as a liquid have no spatial variation; that is, they are each constant over their entire volume. \hyperref[GD:rocTempSimp]{GD: rocTempSimp}. +\item[Newton-Law-Convective-Cooling-Coil-Water:\phantomsection\label{assumpLCCCW}]Newton's law of convective cooling applies between the heating coil and the water. \hyperref[DD:ht.flux.C]{DD: ht\_flux\_C}. +\item[Temp-Heating-Coil-Constant-over-Time:\phantomsection\label{assumpTHCCoT}]The temperature of the heating coil is constant over time. \hyperref[likeChgTCVOD]{LC: Temperature-Coil-Variable-Over-Day} \hyperref[DD:ht.flux.C]{DD: ht\_flux\_C}. +\item[Temp-Heating-Coil-Constant-over-Length:\phantomsection\label{assumpTHCCoL}]The temperature of the heating coil does not vary along its length. \hyperref[likeChgTCVOL]{LC: Temperature-Coil-Variable-Over-Length} \hyperref[DD:ht.flux.C]{DD: ht\_flux\_C}. +\item[Law-Convective-Cooling-Water-PCM:\phantomsection\label{assumpLCCWP}]Newton's law of convective cooling applies between the water and the PCM. \hyperref[DD:ht.flux.P]{DD: ht\_flux\_P}. +\item[Charging-Tank-No-Temp-Discharge:\phantomsection\label{assumpCTNOD}]The model only accounts for charging of the tank, not discharging. The temperature of the water and temperature of the phase change material can only increase, or remain constant; they do not decrease. This implies that the initial temperature \hyperref[assumpSITWP]{A: Same-Initial-Temp-Water-PCM} is less than (or equal) to the temperature of the heating coil. \hyperref[likeChgDT]{LC: Discharging-Tank} \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}. +\item[Same-Initial-Temp-Water-PCM:\phantomsection\label{assumpSITWP}]The initial temperature of the water and the PCM is the same. \hyperref[likeChgDITPW]{LC: Different-Initial-Temps-PCM-Water} \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM} \hyperref[assumpCTNOD]{A: Charging-Tank-No-Temp-Discharge}. +\item[PCM-Initially-Solid:\phantomsection\label{assumpPIS}]The simulation will start with the PCM in a solid state. \hyperref[IM:heatEInPCM]{IM: heatEInPCM} \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}. +\item[Water-Always-Liquid:\phantomsection\label{assumpWAL}]The operating temperature range of the system is such that the water is always in liquid state. That is, the temperature will not drop below the melting point temperature of water, or rise above its boiling point temperature. \hyperref[unlikeChgWPFS]{UC: Water-PCM-Fixed-States} \hyperref[IM:heatEInWtr]{IM: heatEInWtr} \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}. +\item[Perfect-Insulation-Tank:\phantomsection\label{assumpPIT}]The tank is perfectly insulated so that there is no heat loss from the tank. \hyperref[likeChgTLH]{LC: Tank-Lose-Heat} \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}. +\item[No-Internal-Heat-Generation-By-Water-PCM:\phantomsection\label{assumpNIHGBWP}]No internal heat is generated by either the water or the PCM ; therefore, the volumetric heat generation per unit volume is zero. \hyperref[unlikeChgNIHG]{UC: No-Internal-Heat-Generation} \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr} \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}. +\item[Volume-Change-Melting-PCM-Negligible:\phantomsection\label{assumpVCMPN}]The volume change of the PCM due to melting is negligible. \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}. +\item[No-Gaseous-State-PCM:\phantomsection\label{assumpNGSP}]The PCM is either in a liquid state or a solid state but not a gaseous state. \hyperref[unlikeChgWPFS]{UC: Water-PCM-Fixed-States} \hyperref[unlikeChgNGS]{UC: No-Gaseous-State} \hyperref[IM:heatEInPCM]{IM: heatEInPCM} \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}. +\item[Atmospheric-Pressure-Tank:\phantomsection\label{assumpAPT}]The pressure in the tank is atmospheric, so the melting point temperature and boiling point temperature are 0${}^{\circ}$C and 100${}^{\circ}$C, respectively. \hyperref[IM:heatEInWtr]{IM: heatEInWtr} \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}. +\item[Volume-Coil-Negligible:\phantomsection\label{assumpVCN}]When considering the volume of water in the tank, the volume of the heating coil is assumed to be negligible. \hyperref[inputInitQuants]{FR: Input-Initial-Quantities}. +\end{itemize} +\subsubsection{Theoretical Models} +\label{Sec:TMs} +This section focuses on the general equations and laws that SWHS is based on. +\par~ + +\noindent \begin{minipage}{\textwidth} +\begin{tabular}{p{0.2\textwidth} p{0.73\textwidth}} +\toprule \textbf{Refname} & \textbf{TM:consThermE} +\phantomsection +\label{TM:consThermE} +\\ \midrule \\ +Label & Conservation of thermal energy + \\ \midrule \\ + Equation & \begin{displaymath} + -∇\cdot{}\mathbf{q}+g=ρ C \frac{\partial{}\,T}{\partial{}\,t} + \end{displaymath} + \\ \midrule \\ + Description & \begin{symbDescription} + \item{$∇$ is the gradient (Unitless)} + \item{$\mathbf{q}$ is the thermal flux vector ($\frac{\text{W}}{\text{m}^{2}}$)} + \item{$g$ is the volumetric heat generation per unit volume ($\frac{\text{W}}{\text{m}^{3}}$)} + \item{$ρ$ is the density ($\frac{\text{kg}}{\text{m}^{3}}$)} + \item{$C$ is the specific heat capacity ($\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$)} + \item{$t$ is the time (s)} + \item{$T$ is the temperature (${}^{\circ}$C)} + \end{symbDescription} + \\ \midrule \\ + Notes & The above equation gives the law of conservation of energy for transient heat transfer in a material of specific heat capacity $C$ ($\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$) and density, $ρ$ ($\frac{\text{kg}}{\text{m}^{3}}$), where $\mathbf{q}$ is the thermal flux vector ($\frac{\text{W}}{\text{m}^{2}}$), $g$ is the volumetric heat generation per unit volume ($\frac{\text{W}}{\text{m}^{3}}$), $T$ is the temperature (${}^{\circ}$C), $t$ is time (s), and $∇$ is the degree of steepness of a graph at any point. For this equation to apply, other forms of energy, such as mechanical energy, are assumed to be negligible in the system (\hyperref[assumpTEO]{A: Thermal-Energy-Only}). + \\ \midrule \\ + Source & \hyperref{http://www.efunda.com/formulae/heat_transfer/conduction/overview_cond.cfm}{}{}{Fourier Law of Heat Conduction and Heat Equation} + \\ \midrule \\ + RefBy & \hyperref[GD:rocTempSimp]{GD: rocTempSimp}. +\\ \bottomrule \end{tabular} +\end{minipage} +\par~ + +\noindent \begin{minipage}{\textwidth} +\begin{tabular}{p{0.2\textwidth} p{0.73\textwidth}} +\toprule \textbf{Refname} & \textbf{TM:sensHtE} +\phantomsection +\label{TM:sensHtE} +\\ \midrule \\ +Label & Sensible heat energy + \\ \midrule \\ + Equation & \begin{displaymath} + E=\begin{cases} +{C^{S}} m ΔT, & T<{T_{melt}}\\ +{C^{L}} m ΔT, & {T_{melt}}{{T_{melt}}^{P}}\\ +0, & {T_{P}}={{T_{melt}}^{P}}\\ +0, & 0<ϕ<1 +\end{cases} + \end{displaymath} + \\ \midrule \\ + Description & \begin{symbDescription} + \item{$t$ is the time (s)} + \item{${T_{P}}$ is the temperature of the phase change material (${}^{\circ}$C)} + \item{${{τ_{P}}^{S}}$ is the ODE parameter for solid PCM (s)} + \item{${T_{W}}$ is the temperature of the water (${}^{\circ}$C)} + \item{${{τ_{P}}^{L}}$ is the ODE parameter for liquid PCM (s)} + \item{${{T_{melt}}^{P}}$ is the melting point temperature for PCM (${}^{\circ}$C)} + \item{$ϕ$ is the melt fraction (Unitless)} + \end{symbDescription} + \\ \midrule \\ + Notes & ${{T_{melt}}^{P}}$, ${t_{final}}$, ${T_{init}}$, ${h_{P}}$, ${m_{P}}$, ${{C_{P}}^{S}}$, ${{C_{P}}^{S}}$ form (\hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}). The input is constrained so that ${T_{init}}<{{T_{melt}}^{P}}$ (\hyperref[assumpPIS]{A: PCM-Initially-Solid}) ${T_{P}}$, $0{{T_{melt}}^{P}}\\ +{{{E_{P}}_{melt}}^{init}}+{Q_{P}}\left(t\right), & {T_{P}}={{T_{melt}}^{P}}\\ +{{{E_{P}}_{melt}}^{init}}+{Q_{P}}\left(t\right), & 0<ϕ<1 +\end{cases} + \end{displaymath} + \\ \midrule \\ + Description & \begin{symbDescription} + \item{${E_{P}}$ is the change in heat energy in the PCM (J)} + \item{${{C_{P}}^{S}}$ is the specific heat capacity of PCM as a solid ($\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$)} + \item{${m_{P}}$ is the mass of phase change material (kg)} + \item{${T_{P}}$ is the temperature of the phase change material (${}^{\circ}$C)} + \item{$t$ is the time (s)} + \item{${T_{init}}$ is the initial temperature (${}^{\circ}$C)} + \item{${{{E_{P}}_{melt}}^{init}}$ is the change in heat energy in the PCM at the instant when melting begins (J)} + \item{${H_{f}}$ is the specific latent heat of fusion ($\frac{\text{J}}{\text{kg}}$)} + \item{${{C_{P}}^{L}}$ is the specific heat capacity of PCM as a liquid ($\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$)} + \item{${{T_{melt}}^{P}}$ is the melting point temperature for PCM (${}^{\circ}$C)} + \item{${Q_{P}}$ is the latent heat energy added to PCM (J)} + \item{$ϕ$ is the melt fraction (Unitless)} + \end{symbDescription} + \\ \midrule \\ + Notes & The above equation is derived using \hyperref[TM:sensHtE]{TM: sensHtE} and \hyperref[TM:latentHtE]{TM: latentHtE}. ${E_{P}}$ is the change in thermal energy of the PCM relative to the energy at the initial temperature (${T_{init}}$) J. ${E_{P}}$ for the solid PCM is found using \hyperref[TM:sensHtE]{TM: sensHtE} for sensible heat ing, with the specific heat capacity of the solid PCM, ${{C_{P}}^{S}}$ ($\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$) and the change in the PCM temperature from the initial temperature (${}^{\circ}$C). ${E_{P}}$ for the melted PCM (${T_{P}}>{{{E_{P}}_{melt}}^{init}}$) is found using \hyperref[TM:sensHtE]{TM: sensHtE} for sensible heat of the liquid. PCM plus the energy when melting starts, plus the energy required to melt all of the PCM The energy when melting starts is ${{{E_{P}}_{melt}}^{init}}$ (J). The energy required to melt all of the PCM is ${H_{f}} {m_{P}}$ (J) (\hyperref[DD:htFusion]{DD: htFusion}). the specific heat capacity of the liquid PCM is ${{C_{P}}^{L}}$ ($\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$) and the change in temperature is ${T_{P}}-{{T_{melt}}^{P}}$ (${}^{\circ}$C). ${E_{P}}$ during melting of the PCM is found using the energy required at the instant melting of the PCM begins, ${{{E_{P}}_{melt}}^{init}}$ plus the latent heat energy added to the PCM, ${Q_{P}}$ (J) since the time when melting began ${{t_{melt}}^{init}}$ (s). The heat energy for boiling of the PCM is not detailed, since the PCM is assumed to either be in a solid or liquid state (\hyperref[assumpNGSP]{A: No-Gaseous-State-PCM}) (\hyperref[assumpPIS]{A: PCM-Initially-Solid}). + \\ \midrule \\ + Source & \cite{koothoor2013} + \\ \midrule \\ + RefBy & \hyperref[unlikeChgNGS]{UC: No-Gaseous-State} \hyperref[findMass]{FR: Find-Mass} \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM} \hyperref[calcChgHeatEnergyPCMOverTime]{FR: Calculate-Change-Heat\_Energy-PCM-Over-Time}. +\\ \bottomrule \end{tabular} +\end{minipage} +\subsubsection{Data Constraints} +\label{Sec:DataConstraints} +\hyperref[Table:InDataConstraints]{Table:InDataConstraints} and \hyperref[Table:OutDataConstraints]{Table:OutDataConstraints} show the data constraints on the input and output variables, respectively. The column for physical constraints gives the physical limitations on the range of values that can be taken by the variable. The uncertainty column provides an estimate of the confidence with which the physical quantities can be measured. This information would be part of the input if one were performing an uncertainty quantification exercise. The constraints are conservative, to give the user of the model the flexibility to experiment with unusual situations. The column of typical values is intended to provide a feel for a common scenario. The column for software constraints restricts the range of inputs to reasonable values.(*) These quantities cannot be equal to zero, or there will be a divide by zero in the model. (+) These quantities cannot be zero, or there would be freezing (\hyperref[assumpPIS]{A: PCM-Initially-Solid}). (++) The constraints on the surface area are calculated by considering the surface area to volume ratio. The assumption is that the lowest ratio is 1 and the highest possible is $\frac{2}{{h_{min}}}$, where ${h_{min}}$ is the thickness of a ``sheet'' of PCM. A thin sheet has the greatest surface area to volume ratio. (**) The constraint on the maximum time at the end of the simulation is the total number of seconds in one day. +\begin{longtable}{l l l l l} +\toprule +Var & Physical Constraints & Software Constraints & Typical Value & Uncert. +\\ +\midrule +\endhead +${A_{C}}$ & ${A_{C}}>0$ & ${A_{C}}\leq{}{{A_{C}}^{max}}$ & $120.0\cdot{}10^{-3}$ $\text{m}^{2}$ & 10.0$\%$ +\\ +${A_{P}}$ & ${A_{P}}>0$ & ${V_{P}}\leq{}{A_{P}}\leq{}\frac{2}{{h_{min}}} {V_{tank}}$ & $1.2$ $\text{m}^{2}$ & 10.0$\%$ +\\ +${C_{W}}$ & ${C_{W}}>0$ & ${{C_{W}}^{min}}<{C_{W}}<{{C_{W}}^{max}}$ & $4.186\cdot{}10^{3}$ $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ & 10.0$\%$ +\\ +${{C_{P}}^{L}}$ & ${{C_{P}}^{L}}>0$ & ${{{C_{P}}^{L}}_{min}}<{{C_{P}}^{L}}<{{{C_{P}}^{L}}_{max}}$ & $2.27\cdot{}10^{3}$ $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ & 10.0$\%$ +\\ +${{C_{P}}^{S}}$ & ${{C_{P}}^{S}}>0$ & ${{{C_{P}}^{S}}_{min}}<{{C_{P}}^{S}}<{{{C_{P}}^{S}}_{max}}$ & $1.76\cdot{}10^{3}$ $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ & 10.0$\%$ +\\ +$D$ & $D>0$ & -- & $412.0\cdot{}10^{-3}$ m & 10.0$\%$ +\\ +${h_{C}}$ & ${h_{C}}>0$ & ${{h_{C}}^{min}}\leq{}{h_{C}}\leq{}{{h_{C}}^{max}}$ & $1.0\cdot{}10^{3}$ $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ & 10.0$\%$ +\\ +${H_{f}}$ & ${H_{f}}>0$ & ${{H_{f}}_{min}}<{H_{f}}<{{H_{f}}_{max}}$ & $211.6\cdot{}10^{3}$ $\frac{\text{J}}{\text{kg}}$ & 10.0$\%$ +\\ +${h_{P}}$ & ${h_{P}}>0$ & ${{h_{P}}^{min}}\leq{}{h_{P}}\leq{}{{h_{P}}^{max}}$ & $1.0\cdot{}10^{3}$ $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ & 10.0$\%$ +\\ +$L$ & $L>0$ & ${L_{min}}\leq{}L\leq{}{L_{max}}$ & $1.5$ m & 10.0$\%$ +\\ +${T_{C}}$ & $0<{T_{C}}<100$ & -- & $50.0$ ${}^{\circ}$C & 10.0$\%$ +\\ +${t_{final}}$ & ${t_{final}}>0$ & ${t_{final}}<{{t_{final}}^{max}}$ & $50.0\cdot{}10^{3}$ s & 10.0$\%$ +\\ +${T_{init}}$ & $0<{T_{init}}<{T_{melt}}$ & -- & $40.0$ ${}^{\circ}$C & 10.0$\%$ +\\ +${{T_{melt}}^{P}}$ & $0<{{T_{melt}}^{P}}<{T_{C}}$ & -- & $44.2$ ${}^{\circ}$C & 10.0$\%$ +\\ +${V_{P}}$ & $0<{V_{P}}<{V_{tank}}$ & ${V_{P}}\geq{}MINFRACT {V_{tank}}$ & $500.0\cdot{}10^{-3}$ $\text{m}^{3}$ & 10.0$\%$ +\\ +${ρ_{P}}$ & ${{ρ_{P}}^{min}}<{ρ_{P}}<{{ρ_{P}}^{max}}$ & -- & $1.007\cdot{}10^{3}$ $\frac{\text{kg}}{\text{m}^{3}}$ & 10.0$\%$ +\\ +${ρ_{W}}$ & ${ρ_{W}}>0$ & ${{ρ_{W}}^{min}}<{ρ_{W}}\leq{}{{ρ_{W}}^{max}}$ & $1.0\cdot{}10^{3}$ $\frac{\text{kg}}{\text{m}^{3}}$ & 10.0$\%$ +\\ +\bottomrule +\caption{Input Data Constraints} +\label{Table:InDataConstraints} +\end{longtable} +\begin{longtable}{l l} +\toprule +Var & Physical Constraints +\\ +\midrule +\endhead +${T_{W}}$ & ${T_{init}}\leq{}{T_{W}}\leq{}{T_{C}}$ +\\ +${T_{P}}$ & ${T_{init}}\leq{}{T_{P}}\leq{}{T_{C}}$ +\\ +${E_{W}}$ & ${E_{W}}\geq{}0$ +\\ +${E_{P}}$ & ${E_{P}}\geq{}0$ +\\ +\bottomrule +\caption{Output Data Constraints} +\label{Table:OutDataConstraints} +\end{longtable} +\subsubsection{Properties of a Correct Solution} +\label{Sec:CorSolProps} +A correct solution must exhibit the law of conservation of energy. This means that the change in heat energy in the water should equal the difference between the total energy input from the heating coil and the energy output to the PCM. This can be shown as an equation by taking \hyperref[DD:ht.flux.C]{DD: ht\_flux\_C} and \hyperref[DD:ht.flux.P]{DD: ht\_flux\_P}, multiplying each by their respective surface area of heat transfer, and integrating each over the simulation time, as follows: +\begin{displaymath} +{E_{W}}=\int_{0}^{t}{{h_{C}} {A_{C}} \left({T_{C}}-{T_{W}}\left(t\right)\right)}\,dt-\int_{0}^{t}{{h_{P}} {A_{P}} \left({T_{W}}\left(t\right)-{T_{P}}\left(t\right)\right)}\,dt +\end{displaymath} +In addition, the change in heat energy in the PCM should equal the energy input to the PCM from the water. This can be expressed as +\begin{displaymath} +{E_{P}}=\int_{0}^{t}{{h_{P}} {A_{P}} \left({T_{W}}\left(t\right)-{T_{P}}\left(t\right)\right)}\,dt +\end{displaymath} +Equations (FIXME: Equation 7) and (FIXME: Equation 8) can be used as ``sanity'' checks to gain confidence in any solution computed by SWHS. The relative error between the results computed by SWHS and the results calculated from the RHS of these equations should be less than 0.001% \hyperref[verifyEnergyOutput]{FR: Verify-Energy-Output-Follow-Conservation-of-Energy}. +\section{Requirements} +\label{Sec:Requirements} +This section provides the functional requirements, the business tasks that the software is expected to complete, and the non-functional requirements, the qualities that the software is expected to exhibit. +\subsection{Functional Requirements} +\label{Sec:FRs} +\begin{itemize} +\item[Input-Initial-Quantities:\phantomsection\label{inputInitQuants}]Input the following quantities described in \hyperref[Table:Input-Variable-Requirements]{Table:Input-Variable-Requirements}, which define the tank parameters, material properties and initial conditions. \hyperref[assumpVCN]{A: Volume-Coil-Negligible}. +\item[Find-Mass:\phantomsection\label{findMass}]Use the inputs in \hyperref[inputInitQuants]{FR: Input-Initial-Quantities} to find the mass needed for \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}, \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}, \hyperref[IM:heatEInWtr]{IM: heatEInWtr}, and \hyperref[IM:heatEInPCM]{IM: heatEInPCM}, using ${m_{W}}={V_{W}} {ρ_{W}}=\left({V_{tank}}-{V_{P}}\right) {ρ_{W}}=\left(\frac{D}{2} L-{V_{P}}\right) {ρ_{W}}$ and ${m_{P}}={V_{P}} {ρ_{P}}$, where ${V_{W}}$ is the volume of water and ${V_{tank}}$ is the volume of the cylindrical tank. +\item[Check-Input-with-Physical\_Constraints:\phantomsection\label{checkWithPhysConsts}]Verify that the inputs satisfy the required physical constraints. +\item[Output-Input-Derived-Quantities:\phantomsection\label{outputInputDerivQuants}]Output the input quantities and derived quantities in the following list: the quantities from \hyperref[inputInitQuants]{FR: Input-Initial-Quantities}, the masses from \hyperref[findMass]{FR: Find-Mass}, ${τ_{W}}$ (from \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}), $η$ (from \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}), ${{τ_{P}}^{S}}$ (from \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}) and ${{τ_{P}}^{L}}$ (from \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}). +\item[Calculate-Temperature-Water-Over-Time:\phantomsection\label{calcTempWtrOverTime}]Calculate and output the temperature of the water (${T_{W}}$($t$)) over the simulation time (from \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}). +\item[Calculate-Temperature-PCM-Over-Time:\phantomsection\label{calcTempPCMOverTime}]Calculate and output the temperature of the phase change material (${T_{P}}$($t$)) over the simulation time (from \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}). +\item[Calculate-Change-Heat\_Energy-Water-Over-Time:\phantomsection\label{calcChgHeatEnergyWtrOverTime}]Calculate and output the change in heat energy in the water (${E_{W}}$($t$)) over the simulation time (from \hyperref[IM:heatEInWtr]{IM: heatEInWtr}). +\item[Calculate-Change-Heat\_Energy-PCM-Over-Time:\phantomsection\label{calcChgHeatEnergyPCMOverTime}]Calculate and output the change in heat energy in the PCM (${E_{P}}$($t$)) over the simulation time (from \hyperref[IM:heatEInPCM]{IM: heatEInPCM}). +\item[Verify-Energy-Output-Follow-Conservation-of-Energy:\phantomsection\label{verifyEnergyOutput}]Verify that the energy outputs (${E_{W}}$($t$) and ${E_{P}}$($t$)) follow the law of conservation of energy with relative error no greater than 0.001%. +\item[Calculate-PCM-Melt-Begin-Time:\phantomsection\label{calcPCMMeltBegin}]Calculate and output the time at which the PCM begins to melt ${{t_{melt}}^{init}}$ (from \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}). +\item[Calculate-PCM-Melt-End-Time:\phantomsection\label{calcPCMMeltEnd}]Calculate and output the time at which the PCM stops melting ${{t_{melt}}^{final}}$ (from \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}). +\end{itemize} +\begin{longtabu}{l l X[l]} +\toprule +Symbol & Unit & Description +\\ +\midrule +\endhead +$L$ & m & length of tank +\\ +$D$ & m & diameter of tank +\\ +${V_{P}}$ & $\text{m}^{3}$ & volume of PCM +\\ +${A_{P}}$ & $\text{m}^{2}$ & phase change material surface area +\\ +${ρ_{P}}$ & $\frac{\text{kg}}{\text{m}^{3}}$ & density of PCM +\\ +${{T_{melt}}^{P}}$ & ${}^{\circ}$C & melting point temperature for PCM +\\ +${{C_{P}}^{S}}$ & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ & specific heat capacity of PCM as a solid +\\ +${{C_{P}}^{L}}$ & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ & specific heat capacity of PCM as a liquid +\\ +${H_{f}}$ & $\frac{\text{J}}{\text{kg}}$ & specific latent heat of fusion +\\ +${A_{C}}$ & $\text{m}^{2}$ & heating coil surface area +\\ +${T_{C}}$ & ${}^{\circ}$C & temperature of the heating coil +\\ +${ρ_{W}}$ & $\frac{\text{kg}}{\text{m}^{3}}$ & density of water +\\ +${C_{W}}$ & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ & specific heat capacity of water +\\ +${h_{C}}$ & $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ & convective heat transfer coefficient between coil and water +\\ +${h_{P}}$ & $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ & convective heat transfer coefficient between PCM and water +\\ +${T_{init}}$ & ${}^{\circ}$C & initial temperature +\\ +${t_{final}}$ & s & final time +\\ +\bottomrule +\caption{Input Variable Requirements} +\label{Table:Input-Variable-Requirements} +\end{longtabu} +\subsection{Non-Functional Requirements} +\label{Sec:NFRs} +This problem is small in size and relatively simple, so performance is not a priority. Any reasonable implementation will be very quick and use minimal storage. Rather than performance, the non-functional requirement priorities are correctness, verifiability, understandability, reusability, and maintainability. +\section{Likely Changes} +\label{Sec:LCs} +\begin{itemize} +\item[Uniform-Temperature-PCM:\phantomsection\label{likeChgUTP}]\hyperref[assumpTPCAV]{A: Temp-PCM-Constant-Across-Volume} - PCM is actually a poor thermal conductor, so the assumption of uniform temperature of the phase change material is not likely. +\item[Temperature-Coil-Variable-Over-Day:\phantomsection\label{likeChgTCVOD}]\hyperref[assumpTHCCoT]{A: Temp-Heating-Coil-Constant-over-Time} - The temperature of the heating coil will change over the course of the day, depending on the energy received from the sun. +\item[Temperature-Coil-Variable-Over-Length:\phantomsection\label{likeChgTCVOL}]\hyperref[assumpTHCCoL]{A: Temp-Heating-Coil-Constant-over-Length} - The temperature of the heating coil will actually change along its length as the water within it cools. +\item[Discharging-Tank:\phantomsection\label{likeChgDT}]\hyperref[assumpCTNOD]{A: Charging-Tank-No-Temp-Discharge} - The model currently only accounts for charging of the tank. A more complete model would also account for discharging of the tank. +\item[Different-Initial-Temps-PCM-Water:\phantomsection\label{likeChgDITPW}]\hyperref[assumpSITWP]{A: Same-Initial-Temp-Water-PCM} - To add more flexibility to the simulation, the initial temperature of the water and the PCM could be allowed to have different values. +\item[Tank-Lose-Heat:\phantomsection\label{likeChgTLH}]\hyperref[assumpPIT]{A: Perfect-Insulation-Tank} - Any real tank cannot be perfectly insulated and will lose heat. +\end{itemize} +\section{Unlikely Changes} +\label{Sec:UCs} +\begin{itemize} +\item[Water-PCM-Fixed-States:\phantomsection\label{unlikeChgWPFS}]\hyperref[assumpWAL]{A: Water-Always-Liquid} , \hyperref[assumpNGSP]{A: No-Gaseous-State-PCM} - It is unlikely for the change of water from liquid to a solid or the state change of the phase change material from a liquid to a gas to be considered. +\item[No-Internal-Heat-Generation:\phantomsection\label{unlikeChgNIHG}]\hyperref[assumpNIHGBWP]{A: No-Internal-Heat-Generation-By-Water-PCM} - Is used for the derivations of \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr} and \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}. +\item[No-Gaseous-State:\phantomsection\label{unlikeChgNGS}]\hyperref[assumpNGSP]{A: No-Gaseous-State-PCM} - Is used for the derivation of \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM} and for the equation given by \hyperref[IM:heatEInPCM]{IM: heatEInPCM} to be valid. +\end{itemize} +\section{Traceability Matrices and Graphs} +\label{Sec:TraceMatrices} +The purpose of the traceability matrices is to provide easy references on what has to be additionally modified if a certain component is changed. Every time a component is changed, the items in the row of that component that are marked with an ``X'' should be modified as well. \hyperref[Table:Tracey]{Table:Tracey} shows the dependencies of theoretical models, general definitions, data definitions, and instance models with each other. \hyperref[Table:Tracey2]{Table:Tracey2} shows the dependencies of instance models, requirements, and data constraints on each other. \hyperref[Table:Tracey1]{Table:Tracey1} shows the dependencies of theoretical models, general definitions, data definitions, instance models, and likely changes on the assumptions. +\begin{longtable}{l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l} +\toprule + & \hyperref[inputInitQuants]{FR: Input-Initial-Quantities} & \hyperref[IM:heatEInWtr]{IM: heatEInWtr} & \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr} & \hyperref[likeChgDT]{LC: Discharging-Tank} & \hyperref[GD:rocTempSimp]{GD: rocTempSimp} & \hyperref[DD:ht.flux.P]{DD: ht\_flux\_P} & \hyperref[GD:nwtnCooling]{GD: nwtnCooling} & \hyperref[DD:ht.flux.C]{DD: ht\_flux\_C} & \hyperref[unlikeChgWPFS]{UC: Water-PCM-Fixed-States} & \hyperref[unlikeChgNGS]{UC: No-Gaseous-State} & \hyperref[IM:heatEInPCM]{IM: heatEInPCM} & \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM} & \hyperref[unlikeChgNIHG]{UC: No-Internal-Heat-Generation} & \hyperref[likeChgTLH]{LC: Tank-Lose-Heat} & \hyperref[likeChgDITPW]{LC: Different-Initial-Temps-PCM-Water} & \hyperref[assumpCTNOD]{A: Charging-Tank-No-Temp-Discharge} & \hyperref[TM:consThermE]{TM: consThermE} & \hyperref[likeChgTCVOL]{LC: Temperature-Coil-Variable-Over-Length} & \hyperref[likeChgTCVOD]{LC: Temperature-Coil-Variable-Over-Day} & \hyperref[likeChgUTP]{LC: Uniform-Temperature-PCM} & \hyperref[outputInputDerivQuants]{FR: Output-Input-Derived-Quantities} & \hyperref[findMass]{FR: Find-Mass} & \hyperref[calcTempPCMOverTime]{FR: Calculate-Temperature-PCM-Over-Time} & \hyperref[calcPCMMeltEnd]{FR: Calculate-PCM-Melt-End-Time} & \hyperref[calcPCMMeltBegin]{FR: Calculate-PCM-Melt-Begin-Time} & \hyperref[calcTempWtrOverTime]{FR: Calculate-Temperature-Water-Over-Time} & \hyperref[calcChgHeatEnergyPCMOverTime]{FR: Calculate-Change-Heat\_Energy-PCM-Over-Time} & \hyperref[calcChgHeatEnergyWtrOverTime]{FR: Calculate-Change-Heat\_Energy-Water-Over-Time} & \hyperref[DD:melt.frac]{DD: melt\_frac} & \hyperref[TM:latentHtE]{TM: latentHtE} & \hyperref[TM:sensHtE]{TM: sensHtE} +\\ +\midrule +\endhead +\hyperref[Table:Input-Variable-Requirements]{Table:Input-Variable-Requirements} & X & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpAPT]{A: Atmospheric-Pressure-Tank} & & X & X & & & & & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpCTNOD]{A: Charging-Tank-No-Temp-Discharge} & & & X & X & & & & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpCWTAT]{A: Constant-Water-Temp-Across-Tank} & & & & & X & X & & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpDWPCoV]{A: Density-Water-PCM-Constant-over-Volume} & & & & & X & & & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpHTCC]{A: Heat-Transfer-Coeffs-Constant} & & & & & & & X & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpLCCCW]{A: Newton-Law-Convective-Cooling-Coil-Water} & & & & & & & & X & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpLCCWP]{A: Law-Convective-Cooling-Water-PCM} & & & & & & X & & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpNGSP]{A: No-Gaseous-State-PCM} & & & & & & & & & X & X & X & X & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpNIHGBWP]{A: No-Internal-Heat-Generation-By-Water-PCM} & & & X & & & & & & & & & X & X & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpPIS]{A: PCM-Initially-Solid} & & & & & & & & & & & X & X & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpPIT]{A: Perfect-Insulation-Tank} & & & X & & & & & & & & & & & X & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpSHECov]{A: Specific-Heat-Energy-Constant-over-Volume} & & & & & X & & & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpSITWP]{A: Same-Initial-Temp-Water-PCM} & & & & & & & & & & & & X & & & X & X & & & & & & & & & & & & & & & +\\ +\hyperref[assumpTEO]{A: Thermal-Energy-Only} & & & & & & & & & & & & & & & & & X & & & & & & & & & & & & & & +\\ +\hyperref[assumpTHCCoL]{A: Temp-Heating-Coil-Constant-over-Length} & & & & & & & & X & & & & & & & & & & X & & & & & & & & & & & & & +\\ +\hyperref[assumpTHCCoT]{A: Temp-Heating-Coil-Constant-over-Time} & & & & & & & & X & & & & & & & & & & & X & & & & & & & & & & & & +\\ +\hyperref[assumpTPCAV]{A: Temp-PCM-Constant-Across-Volume} & & & & & X & X & & & & & & & & & & & & & & X & & & & & & & & & & & +\\ +\hyperref[assumpVCMPN]{A: Volume-Change-Melting-PCM-Negligible} & & & & & & & & & & & & X & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpVCN]{A: Volume-Coil-Negligible} & X & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[assumpWAL]{A: Water-Always-Liquid} & & X & X & & & & & & X & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[TM:consThermE]{TM: consThermE} & & & & & X & & & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM} & & & X & & & & & & & X & & & X & & & & & & & & X & X & X & X & X & & & & & & +\\ +\hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr} & & & X & & & & & & & & & X & X & & & & & & & & X & X & & & & X & & & & & +\\ +\hyperref[findMass]{FR: Find-Mass} & & & & & & & & & & & & & & & & & & & & & X & & & & & & & & & & +\\ +\hyperref[IM:heatEInPCM]{IM: heatEInPCM} & & & & & & & & & & X & & X & & & & & & & & & & X & & & & & X & & & & +\\ +\hyperref[IM:heatEInWtr]{IM: heatEInWtr} & & & & & & & & & & & & & & & & & & & & & & X & & & & & & X & & & +\\ +\hyperref[DD:htFusion]{DD: htFusion} & & & X & & & & & & & & X & & & & & & & & & & & & & & & & & & X & X & +\\ +\hyperref[DD:ht.flux.C]{DD: ht\_flux\_C} & & & X & & & & & & & & & & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[DD:ht.flux.P]{DD: ht\_flux\_P} & & & X & & & & & & & & & X & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[inputInitQuants]{FR: Input-Initial-Quantities} & & & & & & & & & & & & & & & & & & & & & X & X & & & & & & & & & +\\ +\hyperref[TM:latentHtE]{TM: latentHtE} & & & & & & & & & & & X & & & & & & & & & & & & & & & & & & & & X +\\ +\hyperref[DD:melt.frac]{DD: melt\_frac} & & & X & & & & & & & & & X & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[GD:rocTempSimp]{GD: rocTempSimp} & & & X & & X & & & & & & & X & & & & & & & & & & & & & & & & & & & +\\ +\hyperref[TM:sensHtE]{TM: sensHtE} & & X & & & & & & & & & X & & & & & & & & & & & & & & & & & & & & +\\ +\bottomrule +\caption{Traceability Matrix Showing the Connections Between Items of Different Sections} +\label{Table:Tracey} +\end{longtable} +\begin{longtable}{l l l l l l l l l l l l l l} +\toprule + & T1 (\hyperref[TM:consThermE]{TM: consThermE}) & T2 (\hyperref[TM:sensHtE]{TM: sensHtE}) & T3 (\hyperref[TM:latentHtE]{TM: latentHtE}) & GD1 (\hyperref[GD:nwtnCooling]{GD: nwtnCooling}) & GD2 (\hyperref[GD:rocTempSimp]{GD: rocTempSimp}) & DD1 (\hyperref[DD:ht.flux.C]{DD: ht\_flux\_C}) & DD2 (\hyperref[DD:ht.flux.P]{DD: ht\_flux\_P}) & DD3 (\hyperref[DD:htFusion]{DD: htFusion}) & DD4 (\hyperref[DD:melt.frac]{DD: melt\_frac}) & IM1 (\hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}) & IM2 (\hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}) & IM3 (\hyperref[IM:heatEInWtr]{IM: heatEInWtr}) & IM4 (\hyperref[IM:heatEInPCM]{IM: heatEInPCM}) +\\ +\midrule +\endhead +T1 (\hyperref[TM:consThermE]{TM: consThermE}) & & & & & & & & & & & & & +\\ +T2 (\hyperref[TM:sensHtE]{TM: sensHtE}) & & & X & & & & & & & & & & +\\ +T3 (\hyperref[TM:latentHtE]{TM: latentHtE}) & & & & & & & & & & & & & +\\ +GD1 (\hyperref[GD:nwtnCooling]{GD: nwtnCooling}) & & & & & & & & & & & & & +\\ +GD2 (\hyperref[GD:rocTempSimp]{GD: rocTempSimp}) & X & & & & & & & & & & & & +\\ +DD1 (\hyperref[DD:ht.flux.C]{DD: ht\_flux\_C}) & & & & X & & & & & & & & & +\\ +DD2 (\hyperref[DD:ht.flux.P]{DD: ht\_flux\_P}) & & & & X & & & & & & & & & +\\ +DD3 (\hyperref[DD:htFusion]{DD: htFusion}) & & & & & & & & & & & & & +\\ +DD4 (\hyperref[DD:melt.frac]{DD: melt\_frac}) & & & & & & & & X & & & & & +\\ +IM1 (\hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}) & & & & & X & X & X & & & & X & & +\\ +IM2 (\hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}) & & & & & X & & X & & X & X & & & X +\\ +IM3 (\hyperref[IM:heatEInWtr]{IM: heatEInWtr}) & & X & & & & & & & & & & & +\\ +IM4 (\hyperref[IM:heatEInPCM]{IM: heatEInPCM}) & & X & X & & & & X & X & X & & X & & +\\ +\bottomrule +\caption{Traceability Matrix Showing the Connections Between Items of Different Sections} +\label{Table:Tracey2} +\end{longtable} +\begin{longtable}{l l l l l l l l l l l l l l l l l} +\toprule + & IM1 (\hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}) & IM2 (\hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}) & IM3 (\hyperref[IM:heatEInWtr]{IM: heatEInWtr}) & IM4 (\hyperref[IM:heatEInPCM]{IM: heatEInPCM}) & Data Constraints (\hyperref[Table:InDataConstraints]{Table:InDataConstraints}) & R1 (\hyperref[inputInitQuants]{FR: Input-Initial-Quantities}) & R2 (\hyperref[findMass]{FR: Find-Mass}) & R3 (\hyperref[checkWithPhysConsts]{FR: Check-Input-with-Physical\_Constraints}) & R4 (\hyperref[outputInputDerivQuants]{FR: Output-Input-Derived-Quantities}) & R5 (\hyperref[calcTempWtrOverTime]{FR: Calculate-Temperature-Water-Over-Time}) & R6 (\hyperref[calcTempPCMOverTime]{FR: Calculate-Temperature-PCM-Over-Time}) & R7 (\hyperref[calcChgHeatEnergyWtrOverTime]{FR: Calculate-Change-Heat\_Energy-Water-Over-Time}) & R8 (\hyperref[calcChgHeatEnergyPCMOverTime]{FR: Calculate-Change-Heat\_Energy-PCM-Over-Time}) & R9 (\hyperref[verifyEnergyOutput]{FR: Verify-Energy-Output-Follow-Conservation-of-Energy}) & R10 (\hyperref[calcPCMMeltBegin]{FR: Calculate-PCM-Melt-Begin-Time}) & R11 (\hyperref[calcPCMMeltEnd]{FR: Calculate-PCM-Melt-End-Time}) +\\ +\midrule +\endhead +IM1 (\hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}) & & X & & & & X & X & & & & & & & & & +\\ +IM2 (\hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}) & X & & & X & & X & X & & & & & & & & & +\\ +IM3 (\hyperref[IM:heatEInWtr]{IM: heatEInWtr}) & & & & & & X & X & & & & & & & & & +\\ +IM4 (\hyperref[IM:heatEInPCM]{IM: heatEInPCM}) & & X & & & & X & X & & & & & & & & & +\\ +R1 (\hyperref[inputInitQuants]{FR: Input-Initial-Quantities}) & & & & & & & & & & & & & & & & +\\ +R2 (\hyperref[findMass]{FR: Find-Mass}) & & & & & & X & & & & & & & & & & +\\ +R3 (\hyperref[checkWithPhysConsts]{FR: Check-Input-with-Physical\_Constraints}) & & & & & X & & & & & & & & & & & +\\ +R4 (\hyperref[outputInputDerivQuants]{FR: Output-Input-Derived-Quantities}) & X & X & & & & X & X & & & & & & & & & +\\ +R5 (\hyperref[calcTempWtrOverTime]{FR: Calculate-Temperature-Water-Over-Time}) & X & & & & & & & & & & & & & & & +\\ +R6 (\hyperref[calcTempPCMOverTime]{FR: Calculate-Temperature-PCM-Over-Time}) & & X & & & & & & & & & & & & & & +\\ +R7 (\hyperref[calcChgHeatEnergyWtrOverTime]{FR: Calculate-Change-Heat\_Energy-Water-Over-Time}) & & & X & & & & & & & & & & & & & +\\ +R8 (\hyperref[calcChgHeatEnergyPCMOverTime]{FR: Calculate-Change-Heat\_Energy-PCM-Over-Time}) & & & & X & & & & & & & & & & & & +\\ +R9 (\hyperref[verifyEnergyOutput]{FR: Verify-Energy-Output-Follow-Conservation-of-Energy}) & & & X & X & & & & & & & & & & & & +\\ +R10 (\hyperref[calcPCMMeltBegin]{FR: Calculate-PCM-Melt-Begin-Time}) & & X & & & & & & & & & & & & & & +\\ +R11 (\hyperref[calcPCMMeltEnd]{FR: Calculate-PCM-Melt-End-Time}) & & X & & & & & & & & & & & & & & +\\ +\bottomrule +\caption{Traceability Matrix Showing the Connections Between Requirements and Instance Models} +\label{Table:Tracey1} +\end{longtable} +\begin{longtable}{l l l l l l l l l l l l l l l l l l l l} +\toprule + & A1 (\hyperref[assumpTEO]{A: Thermal-Energy-Only}) & A2 (\hyperref[assumpHTCC]{A: Heat-Transfer-Coeffs-Constant}) & A3 (\hyperref[assumpCWTAT]{A: Constant-Water-Temp-Across-Tank}) & A4 (\hyperref[assumpTPCAV]{A: Temp-PCM-Constant-Across-Volume}) & A5 (\hyperref[assumpDWPCoV]{A: Density-Water-PCM-Constant-over-Volume}) & A6 (\hyperref[assumpSHECov]{A: Specific-Heat-Energy-Constant-over-Volume}) & A7 (\hyperref[assumpLCCCW]{A: Newton-Law-Convective-Cooling-Coil-Water}) & A8 (\hyperref[assumpTHCCoT]{A: Temp-Heating-Coil-Constant-over-Time}) & A9 (\hyperref[assumpTHCCoL]{A: Temp-Heating-Coil-Constant-over-Length}) & A10 (\hyperref[assumpLCCWP]{A: Law-Convective-Cooling-Water-PCM}) & A11 (\hyperref[assumpCTNOD]{A: Charging-Tank-No-Temp-Discharge}) & A12 (\hyperref[assumpSITWP]{A: Same-Initial-Temp-Water-PCM}) & A13 (\hyperref[assumpPIS]{A: PCM-Initially-Solid}) & A14 (\hyperref[assumpWAL]{A: Water-Always-Liquid}) & A15 (\hyperref[assumpPIT]{A: Perfect-Insulation-Tank}) & A16 (\hyperref[assumpNIHGBWP]{A: No-Internal-Heat-Generation-By-Water-PCM}) & A17 (\hyperref[assumpVCMPN]{A: Volume-Change-Melting-PCM-Negligible}) & A18 (\hyperref[assumpNGSP]{A: No-Gaseous-State-PCM}) & A19 (\hyperref[assumpAPT]{A: Atmospheric-Pressure-Tank}) +\\ +\midrule +\endhead +T1 (\hyperref[TM:consThermE]{TM: consThermE}) & X & & & & & & & & & & & & & & & & & & +\\ +T2 (\hyperref[TM:sensHtE]{TM: sensHtE}) & & & & & & & & & & & & & & & & & & & +\\ +T3 (\hyperref[TM:latentHtE]{TM: latentHtE}) & & & & & & & & & & & & & & & & & & & +\\ +GD1 (\hyperref[GD:nwtnCooling]{GD: nwtnCooling}) & & X & & & & & & & & & & & & & & & & & +\\ +GD2 (\hyperref[GD:rocTempSimp]{GD: rocTempSimp}) & & & X & X & X & X & & & & & & & & & & & & & +\\ +DD1 (\hyperref[DD:ht.flux.C]{DD: ht\_flux\_C}) & & & & & & & X & X & X & & & & & & & & & & +\\ +DD2 (\hyperref[DD:ht.flux.P]{DD: ht\_flux\_P}) & & & X & X & & & & & & X & & & & & & & & & +\\ +DD3 (\hyperref[DD:htFusion]{DD: htFusion}) & & & & & & & & & & & & & & & & & & & +\\ +DD4 (\hyperref[DD:melt.frac]{DD: melt\_frac}) & & & & & & & & & & & & & & & & & & & +\\ +IM1 (\hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}) & & & & & & & & & & & X & X & & X & X & X & & & X +\\ +IM2 (\hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM}) & & & & & & & & & & & & X & X & & & X & X & X & +\\ +IM3 (\hyperref[IM:heatEInWtr]{IM: heatEInWtr}) & & & & & & & & & & & & & & X & & & & & X +\\ +IM4 (\hyperref[IM:heatEInPCM]{IM: heatEInPCM}) & & & & & & & & & & & & & X & & & & & X & +\\ +LC1 (\hyperref[likeChgUTP]{LC: Uniform-Temperature-PCM}) & & & & X & & & & & & & & & & & & & & & +\\ +LC2 (\hyperref[likeChgTCVOD]{LC: Temperature-Coil-Variable-Over-Day}) & & & & & & & & X & & & & & & & & & & & +\\ +LC3 (\hyperref[likeChgTCVOL]{LC: Temperature-Coil-Variable-Over-Length}) & & & & & & & & & X & & & & & & & & & & +\\ +LC4 (\hyperref[likeChgDT]{LC: Discharging-Tank}) & & & & & & & & & & & X & & & & & & & & +\\ +LC5 (\hyperref[likeChgDITPW]{LC: Different-Initial-Temps-PCM-Water}) & & & & & & & & & & & & X & & & & & & & +\\ +LC6 (\hyperref[likeChgTLH]{LC: Tank-Lose-Heat}) & & & & & & & & & & & & & & & X & & & & +\\ +\bottomrule +\caption{Traceability Matrix Showing the Connections Between Assumptions and Other Items} +\label{Table:Tracey3} +\end{longtable} +The purpose of the traceability graphs is also to provide easy references on what has to be additionally modified if a certain component is changed. The arrows in the graphs represent dependencies. The component at the tail of an arrow is depended on by the component at the head of that arrow. Therefore, if a component is changed, the components that it points to should also be changed. \hyperref[Figure:TraceyA]{Fig:TraceyA} shows the dependencies of theoretical models, general definitions, data definitions, instance models, likely changes, and assumptions on each other. \hyperref[Figure:TraceyR]{Fig:TraceyR} shows the dependencies of instance models, requirements, and data constraints on each other. +\begin{figure} +\begin{center} +\includegraphics[width=\textwidth]{../../../datafiles/SWHS/ATrace.png} +\caption{Traceability Graph Showing the Connections Between Items of Different Sections} +\label{Figure:TraceyA} +\end{center} +\end{figure} +\begin{figure} +\begin{center} +\includegraphics[width=\textwidth]{../../../datafiles/SWHS/RTrace.png} +\caption{Traceability Graph Showing the Connections Between Instance Models, Requirements, and Data Constraints} +\label{Figure:TraceyR} +\end{center} +\end{figure} +\section{Values of Auxiliary Constants} +\label{Sec:AuxConstants} +This section contains the standard values that are used for calculations in SWHS. +\begin{longtabu}{l X[l] l l} +\toprule +Symbol & Description & Value & Unit +\\ +\midrule +\endhead +${{C_{W}}^{max}}$ & maximum specific heat capacity of water & $4210$ & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${{C_{W}}^{min}}$ & minimum specific heat capacity of water & $4170$ & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${{{C_{P}}^{L}}_{max}}$ & maximum specific heat capacity of PCM as a liquid & $5000$ & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${{{C_{P}}^{L}}_{min}}$ & minimum specific heat capacity of PCM as a liquid & $100$ & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${{{C_{P}}^{S}}_{max}}$ & maximum specific heat capacity of PCM as a solid & $4000$ & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${{{C_{P}}^{S}}_{min}}$ & minimum specific heat capacity of PCM as a solid & $100$ & $\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$ +\\ +${{h_{C}}^{max}}$ & maximum convective heat transfer coefficient between coil and water & $10000$ & $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ +\\ +${{h_{C}}^{min}}$ & minimum convective heat transfer coefficient between coil and water & $10$ & $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ +\\ +${{h_{P}}^{max}}$ & maximum convective heat transfer coefficient between PCM and water & $10000$ & $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ +\\ +${{h_{P}}^{min}}$ & minimum convective heat transfer coefficient between PCM and water & $10$ & $\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$ +\\ +${L_{max}}$ & maximum length of tank & $50$ & m +\\ +${L_{min}}$ & minimum length of tank & $100.0\cdot{}10^{-3}$ & m +\\ +$MINFRACT$ & minimum fraction of the tank volume taken up by the PCM & $1.0\cdot{}10^{-6}$ & -- +\\ +${{t_{final}}^{max}}$ & maximum final time & $86400$ & s +\\ +${{ρ_{P}}^{max}}$ & maximum density of PCM & $20000$ & $\frac{\text{kg}}{\text{m}^{3}}$ +\\ +${{ρ_{P}}^{min}}$ & minimum density of PCM & $500$ & $\frac{\text{kg}}{\text{m}^{3}}$ +\\ +${{ρ_{W}}^{max}}$ & maximum density of water & $1000$ & $\frac{\text{kg}}{\text{m}^{3}}$ +\\ +${{ρ_{W}}^{min}}$ & minimum density of water & $950$ & $\frac{\text{kg}}{\text{m}^{3}}$ +\\ +\bottomrule +\caption{Auxiliary Constants} +\label{Table:TAuxConsts} +\end{longtabu} +\section{References} +\label{Sec:References} +\begin{filecontents*}{bibfile.bib} +@book{bueche1986, +author={Bueche, J. Frederick}, +title={Introduction to Physics for Scientists}, +publisher={McGraw Hill}, +year={1986}, +edition={4}, +address={New York City, New York}} + +@book{incroperaEtAl2007, +author={Incropera, F. P. and Dewitt, D. P. and Bergman, T. L. and Lavine, A. S.}, +title={Fundamentals of Heat and Mass Transfer}, +publisher={John Wiley and Sons}, +year={2007}, +edition={6}, +address={Hoboken, New Jersey}} + +@mastersthesis{koothoor2013, +author={Koothoor, Nirmitha}, +title={A document drive approach to certifying scientific computing software}, +school={McMaster University}, +year={2013}, +address={Hamilton, ON, Canada}} + +@misc{lightstone2012, +author={Lightstone, Marilyn}, +title={Derivation of tank/pcm model}, +year={2012}, +note={From Marilyn Lightstone's Personal Notes}} + +@article{dParnas1972, +author={Parnas, David L.}, +title={On the Criteria To Be Used in Decomposing Systems into Modules}, +journal={Communications of the ACM}, +year={1972}, +pages={"1053-1058"}} + +@article{parnasClements1986, +author={Parnas, David L. and Clements, P. C.}, +title={A rational design process: How and why to fake it}, +journal={IEEE Transactions on Software Engineering}, +year={1986}, +month=feb, +volume={12}, +number={2}, +pages={"251-257"}, +address={Washington, USA}} + +@inproceedings{parnasClements1984, +author={Parnas, David L. and Clements, P. C. and Wiess}, +title={The Modular Structure of Complex Systems}, +booktitle={ICSE '84: Proceedings of the 7th international conference on Software engineering}, +year={1984}, +pages={"408-417"}} + +@inproceedings{smithLai2005, +author={Smith, W. Spencer and Lai, Lei}, +title={A new requirements template for scientific computing}, +booktitle={Proceedings of the First International Workshop on Situational Requirements Engineering Processes - Methods, Techniques and Tools to Support Situation-Specific Requirements Engineering Processes, SREP'05}, +year={2005}, +editor={Agerfalk, PJ and Kraiem, N. and Ralyte, J.}, +address={Paris, France}, +pages={"107-121"}, +note={In conjunction with 13th IEEE International Requirements Engineering Conference,}} +\end{filecontents*} +\nocite{*} +\bibstyle{ieeetr} +\printbibliography[heading=none] +\end{document} diff --git a/code/Website/SWHS_SRS.css b/code/Website/SWHS_SRS.css new file mode 100644 index 0000000000..89605b9598 --- /dev/null +++ b/code/Website/SWHS_SRS.css @@ -0,0 +1,93 @@ +body {min-width: 400px; max-width: 1400px;} +.title {text-align: center;} +.author {text-align: center;} +.paragraph {text-align: justify;} +.cases { + display: inline-block; + vertical-align: middle;} +.case { + float: right; + padding-left: 1em;} +.cases > span { + display: block; + padding-top: 0.1em; + padding-left: 0em;} +.casebr { + display: inline-block; + vertical-align: middle; + margin: 0 0.2em 0.4ex; + text-align: center; + font-size: 500%;} +.caption { + text-align: center; + font-weight: bold; + padding-bottom: 1%; + line-height: 0;} +.fraction { + display: inline-block; + vertical-align: middle; + margin: 0 0.2em 0.4ex; + text-align: center;} +.fraction > span { + display: block; + padding-top: 0.15em;} +.fdn {border-top: thin solid black;} +.table { + text-align: left; + padding-left: 1%; + width: 90%; + margin-bottom: 2%; + margin-top: 2%} +table, th, td { + border-collapse: collapse; + margin-left: auto; + margin-right: auto;} +th, td {border: 1px solid black; padding: 0.5em;} +.tdefn, .ddefn {width: 75%; margin-top: 1%; margin-bottom: 1%;} +.tdefn th {width: 15%;} +.ddefn th {width: 15%;} +.section {width: 80%; margin: 0 auto; text-align: left;} +.code { + display: inline-block; + text-align: left; + font-family: Monaco, Consolas, "Andale Mono","DejaVu Sans Mono", monospace; + font-size: 95%; + line-height: 140%; + white-space: pre; + white-space: pre-wrap; + white-space: -moz-pre-wrap; + white-space: -o-pre-wrap; + background: #faf8f0;} +.list {text-align: left;} +figure { +max-width: 100%; +text-align: center; +font-style: bold; +} +.matrix { + position: relative; + display: inline-table; + margin: 10px; + vertical-align: middle;} +.matrix:before, .matrix:after { + content: ""; + position: absolute; + top: 0; + border: 1px solid #000; + width: 5px; + height: 100%;} +.matrix:before { + left: -5px; + border-right: 0px;} +.matrix:after { + right: -5px; + border-left: 0px;} +.matrix td { + padding: 5px; + text-align: center; + border: 0px;} +ul.hide-list-style { + list-style-type: none;} +ul.hide-list-style-no-indent { + list-style-type: none; +padding: 0;} diff --git a/code/Website/SWHS_SRS.html b/code/Website/SWHS_SRS.html new file mode 100644 index 0000000000..04864e9bce --- /dev/null +++ b/code/Website/SWHS_SRS.html @@ -0,0 +1,10571 @@ + + + + + +Software Requirements Specification for Solar Water Heating Systems Incorporating PCM + + + + + +
+

+Software Requirements Specification for Solar Water Heating Systems Incorporating PCM +

+
+
+

+Thulasi Jegatheesan, Brooks MacLachlan, and W. Spencer Smith +

+
+
+
+

+Reference Material +

+

+This section records information for easy reference. +

+
+
+

+Table of Units +

+

+The unit system used throughout is SI (Système International d'Unités). In addition to the basic units, several derived units are also used. For each unit, the table lists the symbol, a description and the SI name. +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Symbol + +Description +
+°C + +temperature (centigrade) +
+J + +energy (joule) +
+kg + +mass (kilogram) +
+m + +length (metre) +
+s + +time (second) +
+W + +power (watt) +
+
+
+
+
+
+

+Table of Symbols +

+

+The table that follows summarizes the symbols used in this document along with their units. The choice of symbols was made to be consistent with the heat transfer literature and with existing documentation for solar water heating systems. The symbols are listed in alphabetical order. +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Symbol + +Description + +Units +
+AC + +Heating coil surface area + +m2 +
+Ain + +Surface area over which heat is transferred in + +m2 +
+Aout + +Surface area over which heat is transferred out + +m2 +
+AP + +Phase change material surface area + +m2 +
+C + +Specific heat capacity + +J/(kg⋅°C) +
+CL + +Specific heat capacity of a liquid + +J/(kg⋅°C) +
+CS + +Specific heat capacity of a solid + +J/(kg⋅°C) +
+CV + +Specific heat capacity of a vapour + +J/(kg⋅°C) +
+CW + +Specific heat capacity of water + +J/(kg⋅°C) +
+CPL + +Specific heat capacity of PCM as a liquid + +J/(kg⋅°C) +
+CPS + +Specific heat capacity of PCM as a solid + +J/(kg⋅°C) +
+D + +Diameter of tank + +m +
+E + +Sensible heat + +J +
+EP + +Change in heat energy in the PCM + +J +
+EW + +Change in heat energy in the water + +J +
+EPmeltinit + +Change in heat energy in the PCM at the instant when melting begins + +J +
+g + +Volumetric heat generation per unit volume + +W/m3 +
+h + +Convective heat transfer coefficient + +W/(m2⋅°C) +
+hC + +Convective heat transfer coefficient between coil and water + +W/(m2⋅°C) +
+Hf + +Specific latent heat of fusion + +J/kg +
+hmin + +Minimum thickness of a sheet of PCM + +m +
+hP + +Convective heat transfer coefficient between PCM and water + +W/(m2⋅°C) +
+L + +Length of tank + +m +
+m + +Mass + +kg +
+mP + +Mass of phase change material + +kg +
+mW + +Mass of water + +kg +
+n̂ + +Unit outward normal vector for a surface + +-- +
+Q + +Latent heat + +J +
+q + +Heat flux + +W/m2 +
+qC + +Heat flux into the water from the coil + +W/m2 +
+qin + +Heat flux input + +W/m2 +
+qout + +Heat flux output + +W/m2 +
+qP + +Heat flux into the PCM from water + +W/m2 +
+QP + +Latent heat energy added to PCM + +J +
+q + +Thermal flux vector + +W/m2 +
+S + +Surface + +m2 +
+T + +Temperature + +°C +
+t + +Time + +s +
+ΔT + +Change in temperature + +°C +
+Tboil + +Boiling point temperature + +°C +
+TC + +Temperature of the heating coil + +°C +
+Tenv + +Temperature of the environment + +°C +
+tfinal + +Final time + +s +
+Tinit + +Initial temperature + +°C +
+Tmelt + +Melting point temperature + +°C +
+TP + +Temperature of the phase change material + +°C +
+TW + +Temperature of the water + +°C +
+tmeltfinal + +Time at which melting of PCM ends + +s +
+tmeltinit + +Time at which melting of PCM begins + +s +
+TmeltP + +Melting point temperature for PCM + +°C +
+V + +Volume + +m3 +
+VP + +Volume of PCM + +m3 +
+Vtank + +Volume of the cylindrical tank + +m3 +
+VW + +Volume of water + +m3 +
+η + +ODE parameter + +-- +
+ρ + +Density + +kg/m3 +
+ρP + +Density of PCM + +kg/m3 +
+ρW + +Density of water + +kg/m3 +
+τ + +Dummy variable for integration over time + +s +
+τW + +ODE parameter for water + +s +
+τPL + +ODE parameter for liquid PCM + +s +
+τPS + +ODE parameter for solid PCM + +s +
+ϕ + +Melt fraction + +-- +
+∇ + +Gradient + +-- +
+
+
+
+
+
+

+Abbreviations and Acronyms +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Abbreviation + +Full Form +
+A + +Assumption +
+DD + +Data Definition +
+GD + +General Definition +
+GS + +Goal Statement +
+IM + +Instance Model +
+LC + +Likely Change +
+ODE + +Ordinary Differential Equation +
+PCM + +Phase Change Material +
+PS + +Physical System Description +
+R + +Requirement +
+RHS + +Right Hand Side +
+SRS + +Software Requirements Specification +
+SWHS + +Solar Water Heating System +
+T + +Theoretical Model +
+UC + +Unlikely Change +
+Uncert. + +Typical Uncertainty +
+
+
+
+
+
+
+
+

+Introduction +

+

+Due to increasing cost, diminishing availability, and negative environmental impact of fossil fuels, there is a higher demand for renewable energy sources and energy storage technology. Solar water heating systems incorporating phase change material (PCM) use renewable energy sources and provide a novel way of storing energy. Solar water heating systems incorporating PCM improve over the traditional solar water heating systems because of their smaller size. The smaller size is possible because of the ability of PCM to store thermal energy as latent heat, which allows higher thermal energy storage capacity per unit weight. +

+

+The following section provides an overview of the Software Requirements Specification (SRS) for solar water heating systems incorporating PCM. The developed program will be referred to as Solar Water Heating System (SWHS). This section explains the purpose of this document, the scope of the system, the characteristics of the intended reader, and the organization of the document. +

+
+
+

+Purpose of Document +

+

+The main purpose of this document is to describe the modelling of solar water heating systems incorporating PCM. The goal statements and theoretical models used in the SWHS code are provided, with an emphasis on explicitly identifying assumptions and unambiguous definitions. This document is intended to be used as a reference to provide ad hoc access to all information necessary to understand and verify the model. The SRS is abstract because the contents say what problem is being solved, but do not say how to solve it. +

+

+This document will be used as a starting point for subsequent development phases, including writing the design specification and the software verification and validation plan. The design document will show how the requirements are to be realized, including decisions on the numerical algorithms and programming environment. The verification and validation plan will show the steps that will be used to increase confidence in the software documentation and the implementation. Although the SRS fits in a series of documents that follow the so-called waterfall model, the actual development process is not constrained in any way. Even when the waterfall model is not followed, as Parnas and Clements point out parnasClements1986, the most logical way to present the documentation is still to "fake" a rational design process. +

+
+
+
+
+

+Scope of Requirements +

+

+The scope of the requirements includes thermal analysis of a single solar water heating tank incorporating PCM. Given the appropriate inputs, SWHS predicts the temperature and thermal energy histories for the water and the PCM. This entire document is written assuming that the substances inside the solar water heating tank are water and PCM. +

+
+
+
+
+

+Characteristics of Intended Reader +

+

+Reviewers of this documentation should have an understanding of heat transfer theory from level 3 or 4 mechanical engineering and differential equations from level 1 and 2 calculus. The users of SWHS can have a lower level of expertise, as explained in Section: User Characteristics. +

+
+
+
+
+

+Organization of Document +

+

+The organization of this document follows the template for an SRS for scientific computing software proposed by dParnas1972 and parnasClements1984. The presentation follows the standard pattern of presenting goals, theories, definitions, and assumptions. For readers that would like a more bottom up approach, they can start reading the instance models in Section: Instance Models and trace back to find any additional information they require. +

+

+The goal statements (Section: Goal Statements) are refined to the theoretical models, and the theoretical models (Section: Theoretical Models) to the instance models (Section: Instance Models). The instance models to be solved are referred to as IM: eBalanceOnWtr, IM: eBalanceOnPCM, IM: heatEInWtr, and IM: heatEInPCM. The instance models provide the Ordinary Differential Equation (ODEs) and algebraic equations that model the solar water heating systems incorporating PCM. SWHS solves these ODEs. +

+
+
+
+
+
+
+

+General System Description +

+

+This section provides general information about the system. It identifies the interfaces between the system and its environment, describes the user characteristics, and lists the system constraints. +

+
+
+

+System Context +

+

+Fig:SysCon shows the system context. A circle represents an external entity outside the software, the user in this case. A rectangle represents the software system itself (SWHS). Arrows are used to show the data flow between the system and its environment. +

+
+
+<a href=#Figure:SysCon>Fig:SysCon</a>: System Context +
+Fig:SysCon: System Context +
+
+
+

+SWHS is mostly self-contained. The only external interaction is through the user interface. The responsibilities of the user and the system are as follows: +

+
    +
  • +User Responsibilities: +
      +
    • +Provide the input data to the system, ensuring no errors in the data entry +
      • +
    • +Take care that consistent units are used for input variables +
      • +
    +
    • +
  • +SWHS Responsibilities: +
      +
    • +Detect data type mismatch, such as a string of characters instead of a floating point number +
      • +
    • +Determine if the inputs satisfy the required physical and software constraints +
      • +
    • +Calculate the required outputs +
      • +
    +
    • +
+
+
+
+
+

+User Characteristics +

+

+The end user of SWHS should have an understanding of undergraduate Level 1 Calculus and Physics. +

+
+
+
+
+

+System Constraints +

+

+There are no system constraints. +

+
+
+
+
+
+
+

+Specific System Description +

+

+This section first presents the problem description, which gives a high-level view of the problem to be solved. This is followed by the solution characteristics specification, which presents the assumptions, theories, and definitions that are used. +

+
+
+

+Problem Description +

+

+SWHS is a computer program developed to investigate the effect of employing PCM within a solar water heating tank. +

+
+
+

+Terminology and Definitions +

+

+This subsection provides a list of terms that are used in the subsequent sections and their meaning, with the purpose of reducing ambiguity and making it easier to correctly understand the requirements. +

+
    +
  • +Heat flux: The rate of thermal energy transfer through a given surface per unit time. +
    • +
  • +Phase change material: A substance that uses phase changes (such as melting) to absorb or release large amounts of heat at a constant temperature. +
    • +
  • +Specific heat capacity: The amount of energy required to raise the temperature of the unit mass of a given substance by a given amount. +
    • +
  • +Thermal conduction: The transfer of heat energy through a substance. +
    • +
  • +Transient: Changing with time. +
    • +
+
+
+
+
+

+Physical System Description +

+

+The physical system of SWHS, as shown in Fig:Tank, includes the following elements: +

+
+

+PS1: Tank containing water. +

+

+PS2: Heating coil at bottom of tank. (qC represents the heat flux into the water from the coil.) +

+

+PS3: PCM suspended in tank. (qP represents the heat flux into the PCM from water.) +

+
+
+
+Solar water heating tank, with heat flux into the water from the coil of <em>q<sub>C</sub></em> and heat flux into the PCM from water of <em>q<sub>P</sub></em> +
+Solar water heating tank, with heat flux into the water from the coil of qC and heat flux into the PCM from water of qP +
+
+
+
+
+
+
+

+Goal Statements +

+

+Given the temperature of the heating coil, initial conditions for the temperature of the water and the temperature of the phase change material, and material properties, the goal statements are: +

+
+

+GS1: Predict the temperature of the water over time. +

+

+GS2: Predict the temperature of the phase change material over time. +

+

+GS3: Predict the change in heat energy in the water over time. +

+

+GS4: Predict the change in heat energy in the PCM over time. +

+
+
+
+
+
+
+
+

+Solution Characteristics Specification +

+

+The instance models that govern SWHS are presented in Section: Instance Models. The information to understand the meaning of the instance models and their derivation is also presented, so that the instance models can be verified. +

+
+
+

+Assumptions +

+

+This section simplifies the original problem and helps in developing the theoretical model by filling in the missing information for the physical system. The numbers given in the square brackets refer to the Theoretical Models Section: Theoretical Models, General Definitions Section: General Definitions, Data Definitions Section: Data Definitions, Instance Models Section: Instance Models, Likely Changes Section: Likely Changes, or Unlikely Changes Section: Unlikely Changes, in which the respective assumption is used. +

+
+

+

+Thermal-Energy-Only: The only form of energy that is relevant for this problem is thermal energy. All other forms of energy, such as mechanical energy, are assumed to be negligible. TM: consThermE. +
+

+

+

+Heat-Transfer-Coeffs-Constant: All heat transfer coefficients are constant over time. GD: nwtnCooling. +
+

+

+

+Constant-Water-Temp-Across-Tank: The water in the tank is fully mixed, so the temperature of the water is the same throughout the entire tank. GD: rocTempSimp DD: ht_flux_P. +
+

+

+

+Temp-PCM-Constant-Across-Volume: The temperature of the phase change material is the same throughout the volume of PCM. GD: rocTempSimp LC: Uniform-Temperature-PCM DD: ht_flux_P. +
+

+

+

+Density-Water-PCM-Constant-over-Volume: The density of water and density of PCM have no spatial variation; that is, they are each constant over their entire volume. GD: rocTempSimp. +
+

+

+

+Specific-Heat-Energy-Constant-over-Volume: The specific heat capacity of water, specific heat capacity of PCM as a solid, and specific heat capacity of PCM as a liquid have no spatial variation; that is, they are each constant over their entire volume. GD: rocTempSimp. +
+

+

+

+Newton-Law-Convective-Cooling-Coil-Water: Newton's law of convective cooling applies between the heating coil and the water. DD: ht_flux_C. +
+

+

+

+Temp-Heating-Coil-Constant-over-Time: The temperature of the heating coil is constant over time. LC: Temperature-Coil-Variable-Over-Day DD: ht_flux_C. +
+

+

+

+Temp-Heating-Coil-Constant-over-Length: The temperature of the heating coil does not vary along its length. LC: Temperature-Coil-Variable-Over-Length DD: ht_flux_C. +
+

+

+

+Law-Convective-Cooling-Water-PCM: Newton's law of convective cooling applies between the water and the PCM. DD: ht_flux_P. +
+

+

+

+Charging-Tank-No-Temp-Discharge: The model only accounts for charging of the tank, not discharging. The temperature of the water and temperature of the phase change material can only increase, or remain constant; they do not decrease. This implies that the initial temperature A: Same-Initial-Temp-Water-PCM is less than (or equal) to the temperature of the heating coil. LC: Discharging-Tank IM: eBalanceOnWtr. +
+

+

+

+Same-Initial-Temp-Water-PCM: The initial temperature of the water and the PCM is the same. LC: Different-Initial-Temps-PCM-Water IM: eBalanceOnPCM A: Charging-Tank-No-Temp-Discharge. +
+

+

+

+PCM-Initially-Solid: The simulation will start with the PCM in a solid state. IM: heatEInPCM IM: eBalanceOnPCM. +
+

+

+

+Water-Always-Liquid: The operating temperature range of the system is such that the water is always in liquid state. That is, the temperature will not drop below the melting point temperature of water, or rise above its boiling point temperature. UC: Water-PCM-Fixed-States IM: heatEInWtr IM: eBalanceOnWtr. +
+

+

+

+Perfect-Insulation-Tank: The tank is perfectly insulated so that there is no heat loss from the tank. LC: Tank-Lose-Heat IM: eBalanceOnWtr. +
+

+

+

+No-Internal-Heat-Generation-By-Water-PCM: No internal heat is generated by either the water or the PCM ; therefore, the volumetric heat generation per unit volume is zero. UC: No-Internal-Heat-Generation IM: eBalanceOnWtr IM: eBalanceOnPCM. +
+

+

+

+Volume-Change-Melting-PCM-Negligible: The volume change of the PCM due to melting is negligible. IM: eBalanceOnPCM. +
+

+

+

+No-Gaseous-State-PCM: The PCM is either in a liquid state or a solid state but not a gaseous state. UC: Water-PCM-Fixed-States UC: No-Gaseous-State IM: heatEInPCM IM: eBalanceOnPCM. +
+

+

+

+Atmospheric-Pressure-Tank: The pressure in the tank is atmospheric, so the melting point temperature and boiling point temperature are 0°C and 100°C, respectively. IM: heatEInWtr IM: eBalanceOnWtr. +
+

+

+

+Volume-Coil-Negligible: When considering the volume of water in the tank, the volume of the heating coil is assumed to be negligible. FR: Input-Initial-Quantities. +
+

+
+
+
+
+
+

+Theoretical Models +

+

+This section focuses on the general equations and laws that SWHS is based on. +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Conservation of thermal energy +

+
+Equation + +
+−∇⋅q+g = ρ C 
+ +∂ T + + +∂ t + +
 +
+
+Description + +
    +
  • +∇ is the gradient (Unitless) +
    • +
  • +q is the thermal flux vector (W/m2) +
    • +
  • +g is the volumetric heat generation per unit volume (W/m3) +
    • +
  • +ρ is the density (kg/m3) +
    • +
  • +C is the specific heat capacity (J/(kg⋅°C)) +
    • +
  • +t is the time (s) +
    • +
  • +T is the temperature (°C) +
    • +
+
+Notes + +

+The above equation gives the law of conservation of energy for transient heat transfer in a material of specific heat capacity C (J/(kg⋅°C)) and density, ρ (kg/m3), where q is the thermal flux vector (W/m2), g is the volumetric heat generation per unit volume (W/m3), T is the temperature (°C), t is time (s), and ∇ is the degree of steepness of a graph at any point. For this equation to apply, other forms of energy, such as mechanical energy, are assumed to be negligible in the system (A: Thermal-Energy-Only). +

+
+Source + +

+Fourier Law of Heat Conduction and Heat Equation +

+
+RefBy + +

+GD: rocTempSimp. +

+
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Sensible heat energy +

+
+Equation + +
+E = +{ + +
+ +CS m ΔT , +T < Tmelt + + + +CL m ΔT , +Tmelt < T < Tboil + + + +CV m ΔT , +Tboil < T + + +
 +
+
+Description + +
    +
  • +E is the sensible heat (J) +
    • +
  • +CS is the specific heat capacity of a solid (J/(kg⋅°C)) +
    • +
  • +m is the mass (kg) +
    • +
  • +ΔT is the change in temperature (°C) +
    • +
  • +CL is the specific heat capacity of a liquid (J/(kg⋅°C)) +
    • +
  • +CV is the specific heat capacity of a vapour (J/(kg⋅°C)) +
    • +
  • +T is the temperature (°C) +
    • +
  • +Tmelt is the melting point temperature (°C) +
    • +
  • +Tboil is the boiling point temperature (°C) +
    • +
+
+Notes + +

+E is the change in sensible heat energy (J). CS, CL, CV are the specific heat capacity of a solid, specific heat capacity of a liquid, and specific heat capacity of a vapour, respectively (J/(kg⋅°C)). m is the mass (kg). T is the temperature (°C), and ΔT is the change in temperature (°C). Tmelt and Tboil are the melting point temperature and boiling point temperature, respectively (°C). Sensible heating occurs as long as the material does not reach a temperature where a phase change occurs. A phase change occurs if T=Tboil or T= Tmelt. If this is the case, refer to TM: latentHtE, Latent heat energy. +

+
+Source + +

+Definition of Sensible Heat +

+
+RefBy + +

+IM: heatEInWtr IM: heatEInPCM IM: heatEInPCM IM: heatEInPCM. +

+
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Latent heat energy +

+
+Equation + +
+Q(t) = ∫0t
+ +d Q(τ) + + +d τ + +
 dτ +
+
+Description + +
    +
  • +Q is the latent heat (J) +
    • +
  • +t is the time (s) +
    • +
  • +τ is the dummy variable for integration over time (s) +
    • +
+
+Notes + +

+Q is the change in thermal energy (J), latent heat energy. Q(t) = ∫0t

+ +d Q(τ) + + +d τ + +
 dτ is the rate of change of Q with respect to time τ (s). t is the time (s) elapsed, as long as the phase change is not complete. The status of the phase change depends on the melt fraction, DD: htFusion. Tmelt and Tboil are the melting point temperature and boiling point temperature, respectively (°C). Latent heating stops when all material has changed to the new phase. +

+
+Source + +

+Definition of Latent Heat +

+
+RefBy + +

+TM: sensHtE IM: heatEInPCM. +

+
+
+
+
+
+
+

+General Definitions +

+

+This section collects the laws and equations that will be used to build the instance models. +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Newton's law of cooling +

+
+Units + +

+W/m2 +

+
+Equation + +
+q(t) = h ΔT(t) +
+
+Description + +
    +
  • +q is the heat flux (W/m2) +
    • +
  • +t is the time (s) +
    • +
  • +h is the convective heat transfer coefficient (W/(m2⋅°C)) +
    • +
  • +ΔT is the change in temperature (°C) +
    • +
+
+Notes + +

+Newton's law of cooling describes convective cooling from a surface. The law is stated as: the rate of heat loss from a body is proportional to the difference in temperatures between the body and its surroundings. q(t) is the thermal flux (W/m2). h is the heat transfer coefficient, assumed independant of T (A: Heat-Transfer-Coeffs-Constant) (W/(m2⋅°C)). ΔT(t) = T(t)−Tenv(t) is the time-dependant thermal gradient between the environment and the object (°C). +

+
+Source + +

+incroperaEtAl2007 +

+
+RefBy + +

+ +

+
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Simplified rate of change of temperature +

+
+Equation + +
+m C 
+ +d T + + +d t + +
= qin Ain−qout Aout+g V +
+
+Description + +
    +
  • +m is the mass (kg) +
    • +
  • +C is the specific heat capacity (J/(kg⋅°C)) +
    • +
  • +t is the time (s) +
    • +
  • +T is the temperature (°C) +
    • +
  • +qin is the heat flux input (W/m2) +
    • +
  • +Ain is the surface area over which heat is transferred in (m2) +
    • +
  • +qout is the heat flux output (W/m2) +
    • +
  • +Aout is the surface area over which heat is transferred out (m2) +
    • +
  • +g is the volumetric heat generation per unit volume (W/m3) +
    • +
  • +V is the volume (m3) +
    • +
+
+Notes + +

+The basic equation governing the rate of change of temperature, for a given volume V, with time. m is the mass (kg). C is the specific heat capacity (J/(kg⋅°C)). T is the temperature (°C) and t is the time (s). qin and qout are the in and out heat transfer rates, respectively (W/m2). Ain and Aout are the surface areas over which the heat is being transferred in and out, respectively (m2). g is the volumetric heat generated (W/m3). V is the volume (m3). +

+
+Source + +

+ +

+
+RefBy + +

+GD: rocTempSimp IM: eBalanceOnWtr IM: eBalanceOnPCM. +

+
+
+

+Detailed derivation of simplified rate of change of temperature : +

+

+Integrating TM: consThermE over a volume (V), we have: +

+
+−∫V∇⋅q dV+∫Vg dV = ∫Vρ C 
+ +∂ T + + +∂ t + +
 dV +
+

+Applying Gauss's Divergence Theorem to the first term over the surface S of the volume, with q as the thermal flux vector for the surface and n̂ as a unit outward normal vector for a surface: +

+
+−∫Sq⋅n̂ dS+∫Vg dV = ∫Vρ C 
+ +∂ T + + +∂ t + +
 dV +
+

+We consider an arbitrary volume. The volumetric heat generation per unit volume is assumed constant. Then (1) can be written as: +

+
+qin Ain−qout Aout+g V = ∫Vρ C 
+ +∂ T + + +∂ t + +
 dV +
+

+Where qin, qout, Ain, and Aout are explained in GD: rocTempSimp. Assuming ρ, C and T are constant over the volume, which is true in our case by A: Constant-Water-Temp-Across-Tank, A: Temp-PCM-Constant-Across-Volume, A: Density-Water-PCM-Constant-over-Volume, and A: Specific-Heat-Energy-Constant-over-Volume, we have: +

+
+ρ C V 
+ +d T + + +d t + +
= qin Ain−qout Aout+g V +
+

+Using the fact that ρ=m/V, (2) can be written as: +

+
+m C 
+ +d T + + +d t + +
= qin Ain−qout Aout+g V +
+
+
+
+
+

+Data Definitions +

+

+This section collects and defines all the data needed to build the instance models. +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Heat flux into the water from the coil +

+
+Symbol + +

+qC +

+
+Units + +

+W/m2 +

+
+Equation + +
+qC = hC (TC−TW(t)) +
+
+Description + +
    +
  • +qC is the heat flux into the water from the coil (W/m2) +
    • +
  • +hC is the convective heat transfer coefficient between coil and water (W/(m2⋅°C)) +
    • +
  • +TC is the temperature of the heating coil (°C) +
    • +
  • +TW is the temperature of the water (°C) +
    • +
  • +t is the time (s) +
    • +
+
+Notes + +

+A: Newton-Law-Convective-Cooling-Coil-Water +

+

+A: Temp-Heating-Coil-Constant-over-Time +

+

+A: Temp-Heating-Coil-Constant-over-Length +

+
+Source + +

+koothoor2013 +

+
+RefBy + +

+IM: eBalanceOnWtr. +

+
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Heat flux into the PCM from water +

+
+Symbol + +

+qP +

+
+Units + +

+W/m2 +

+
+Equation + +
+qP = hP (TW(t)−TP(t)) +
+
+Description + +
    +
  • +qP is the heat flux into the PCM from water (W/m2) +
    • +
  • +hP is the convective heat transfer coefficient between PCM and water (W/(m2⋅°C)) +
    • +
  • +TW is the temperature of the water (°C) +
    • +
  • +t is the time (s) +
    • +
  • +TP is the temperature of the phase change material (°C) +
    • +
+
+Notes + +

+A: Constant-Water-Temp-Across-Tank +

+

+A: Temp-PCM-Constant-Across-Volume +

+

+A: Law-Convective-Cooling-Water-PCM +

+
+Source + +

+koothoor2013 +

+
+RefBy + +

+IM: eBalanceOnWtr IM: eBalanceOnPCM. +

+
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Specific latent heat of fusion +

+
+Symbol + +

+Hf +

+
+Units + +

+J/kg +

+
+Equation + +
+Hf =
+ +Q + + +m + +
 +
+
+Description + +
    +
  • +Hf is the specific latent heat of fusion (J/kg) +
    • +
  • +Q is the latent heat (J) +
    • +
  • +m is the mass (kg) +
    • +
+
+Source + +

+bueche1986 +

+
+RefBy + +

+DD: melt_frac TM: latentHtE IM: heatEInPCM IM: eBalanceOnWtr IM: eBalanceOnWtr. +

+
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Melt fraction +

+
+Symbol + +

+ϕ +

+
+Units + +

+Unitless +

+
+Equation + +
+ϕ =
+ +QP + + +Hf mP + +
 +
+
+Description + +
    +
  • +ϕ is the melt fraction (Unitless) +
    • +
  • +QP is the latent heat energy added to PCM (J) +
    • +
  • +Hf is the specific latent heat of fusion (J/kg) +
    • +
  • +mP is the mass of phase change material (kg) +
    • +
+
+Notes + +

+DD: htFusion +

+
+Source + +

+koothoor2013 +

+
+RefBy + +

+IM: eBalanceOnWtr IM: eBalanceOnPCM. +

+
+
+
+
+
+
+

+Instance Models +

+

+This section transforms the problem defined in Section: Problem Description into one which is expressed in mathematical terms. It uses concrete symbols defined in Section: Data Definitions to replace the abstract symbols in the models identified in Section: Theoretical Models and Section: General Definitions. +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Energy balance on water to find the temperature of the water +

+
+Input + +

+mW, CW, hC, AP, hP, AC, TP, tfinal, TC, Tinit +

+
+Output + +

+TW +

+
+Input Constraints + +
+Tinit < TC +
+
+Output Constraints + +
+0 < t < tfinal +
+
+Equation + +
+
+ +d TW + + +d t + +
=
+ +1 + + +τW + +
 (TC−TW(t)+η (TP(t)−TW(t))) +
+
+Description + +
    +
  • +t is the time (s) +
    • +
  • +TW is the temperature of the water (°C) +
    • +
  • +τW is the ODE parameter for water (s) +
    • +
  • +TC is the temperature of the heating coil (°C) +
    • +
  • +η is the ODE parameter (Unitless) +
    • +
  • +TP is the temperature of the phase change material (°C) +
    • +
+
+Notes + +

+τW, tfinal, TC, TP from (IM: eBalanceOnPCM). The input is constrained so that Tinit ≤ TC. (A: Charging-Tank-No-Temp-Discharge) TW is the temperature of the water (°C). TP is the temperature of the phase change material (°C). TC is the temperature of the heating coil (°C). τW =

+ +mW CW + + +hC AC + +
is a constant (DD: htFusion) (s). η =
+ +hP AP + + +hC AC + +
 is a constant (dimensionless). The above equation applies as long as the water is in liquid form, 0 < TW < 100 (°C) where 0 (°C) and 100 (°C) are the melting and boiling point temperatures of water, respectively (A: Water-Always-Liquid, A: Atmospheric-Pressure-Tank). +

+
+Source + +

+koothoor2013 +

+
+RefBy + +

+UC: No-Internal-Heat-Generation FR: Output-Input-Derived-Quantities FR: Output-Input-Derived-Quantities FR: Find-Mass IM: eBalanceOnWtr IM: eBalanceOnPCM FR: Calculate-Temperature-Water-Over-Time. +

+
+
+

+Derivation of the energy balance on water: +

+

+To find the rate of change of TW, we look at the energy balance on water. The volume being considered is the volume of water VW, which has mass of water mW and specific heat capacity of water, CW. qC represents the heat transfer into the water from the heating coil and qP represents the heat transfer into the PCM from water, over heating coil surface area and phase change material surface area of AC and AP, respectively. No heat transfer occurs to the outside of the tank, since it has been assumed to be perfectly insulated (A: Perfect-Insulation-Tank). Assuming no volumetric heat generation per unit volume (A: No-Internal-Heat-Generation-By-Water-PCM), g = 0. Therefore, the equation for GD: rocTempSimp can be written as: +

+
+mW CW 
+ +d TW + + +d t + +
= qC AC−qP AP +
+

+Using DD: ht_flux_C and DD: ht_flux_P for qC and qP respectively, this can be written as: +

+
+mW CW 
+ +d TW + + +d t + +
= hC AC (TC−TW)−hP AP (TW−TP) +
+

+Dividing (3) by mWCW, we obtain: +

+
+
+ +d TW + + +d t + +
=
+ +hC AC + + +mW CW + +
 (TC−TW)−
+ +mP AP + + +mW CW + +
 (TW−TP) +
+

+Factoring the negative sign out of the second term of the RHS of Equation (4) and multiplying it by hC AC / hC AC yields: +

+
+
+ +d TW + + +d t + +
=
+ +hC AC + + +mW CW + +
 (TC−TW)+
+ +hC AC + + +hC AC + +
 
+ +hP AP + + +mW CW + +
 (TP−TW) +
+

+Which simplifies to: +

+
+
+ +d TW + + +d t + +
=
+ +hC AC + + +mW CW + +
 (TC−TW)+
+ +hP AP + + +hC AC + +
 
+ +hC AC + + +mW CW + +
 (TP−TW) +
+

+Setting τW =

+ +mW CW + + +hC AC + +
(DD: htFusion) and η =
+ +hP AP + + +hC AC + +
 (DD: melt_frac), Equation (5) can be written as: +

+
+
+ +d TW + + +d t + +
=
+ +1 + + +τW + +
 (TC−TW)+
+ +η + + +τW + +
 (TP−TW) +
+

+Finally, factoring out

+ +1 + + +τW + +
, we are left with the governing ODE for (IM: eBalanceOnWtr): +

+
+
+ +d TW + + +d t + +
=
+ +1 + + +τW + +
 (TC−TW+η (TP−TW)) +
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Energy Balance on PCM to Find T_p +

+
+Input + +

+TmeltP, tfinal, Tinit, AP, hP, mP, CPS, CPL +

+
+Output + +

+TP +

+
+Input Constraints + +
+Tinit < TmeltP +
+
+Output Constraints + +
+0 < t < tfinal +
+
+Equation + +
+
+ +d TP + + +d t + +
= +{ + +
+ +
+ +1 + + +τPS + +
 (TW(t)−TP(t)) , +TP < TmeltP + + + +
+ +1 + + +τPL + +
 (TW(t)−TP(t)) , +TP > TmeltP + + + +0 , +TP = TmeltP + + + +0 , +0 < ϕ < 1 + + +
 +
+
+Description + +
    +
  • +t is the time (s) +
    • +
  • +TP is the temperature of the phase change material (°C) +
    • +
  • +τPS is the ODE parameter for solid PCM (s) +
    • +
  • +TW is the temperature of the water (°C) +
    • +
  • +τPL is the ODE parameter for liquid PCM (s) +
    • +
  • +TmeltP is the melting point temperature for PCM (°C) +
    • +
  • +ϕ is the melt fraction (Unitless) +
    • +
+
+Notes + +

+TmeltP, tfinal, Tinit, hP, mP, CPS, CPS form (IM: eBalanceOnWtr). The input is constrained so that Tinit < TmeltP (A: PCM-Initially-Solid) TP, 0 < t < tfinal, with initial conditions, TW = TP = Tinit, FIXME t_w(0) = t_p(0), A: Same-Initial-Temp-Water-PCM, and TW from IM1, such that the following governing ODE is satisfied. The temperature remains constant at TmeltP, even with the heating (or cool-ing), until the phase change has occurred for all of the material; that is as long as 0 < ϕ < 1 (from DD: melt_frac ) is determined as part of the heat energy in the PCM, as given in (IM: heatEInPCM). +

+
+Source + +

+koothoor2013 +

+
+RefBy + +

+UC: No-Internal-Heat-Generation UC: No-Gaseous-State FR: Output-Input-Derived-Quantities FR: Output-Input-Derived-Quantities FR: Find-Mass IM: eBalanceOnWtr FR: Calculate-Temperature-PCM-Over-Time FR: Calculate-PCM-Melt-End-Time FR: Calculate-PCM-Melt-Begin-Time. +

+
+
+

+Detailed derivation of the energy balance on the PCM during sensible heating phase: +

+

+To find the rate of change of TP, we look at the energy balance on the PCM. The volume being considered is the volume of PCM, VP. The derivation that follows is initially for the solid PCM. The mass of phase change material is mP and the specific heat capacity of PCM as a solid is CPS. The heat flux into the PCM from water is qP over phase change material surface area AP. There is no heat flux output. Assuming no volumetric heat generation per unit volume (A: No-Internal-Heat-Generation-By-Water-PCM), g = 0 , the equation for GD: rocTempSimp can be written as: +

+
+mP CPS 
+ +d TP + + +d t + +
= qP AP +
+

+Using DD: ht_flux_P for qP, this equation can be written as: +

+
+mP CPS 
+ +d TP + + +d t + +
= hP AP (TW−TP) +
+

+Dividing by mP CPS we obtain: +

+
+
+ +d TP + + +d t + +
=
+ +hP AP + + +mP CPS + +
 (TW−TP) +
+

+Setting τPS = mP CPS / hP AP , this can be written as: +

+
+
+ +d TP + + +d t + +
=
+ +1 + + +τPS + +
 (TW−TP) +
+

+Equation (6) applies for the solid PCM. In the case where all of the PCM is melted, the same derivation applies, except that CPS is replaced by CPL, and thus τPS is replaced by τPL. Although a small change in surface area would be expected with melting, this is not included, since the volume change of the PCM with melting is assumed to be negligible (A: Volume-Change-Melting-PCM-Negligible). +

+

+In the case where TP = TmeltP and not all of the PCM is melted, the temperature of the phase change material does not change. Therefore, in this case d TP / d t = 0. +

+

+This derivation does not consider the boiling of the PCM, as the PCM is assumed to either be in a solid state or a liquid state (A: No-Gaseous-State-PCM). +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Heat energy in the water +

+
+Input + +

+Tinit, mW, CW, mW +

+
+Output + +

+EW +

+
+Input Constraints + +
+Output Constraints + +
+0 < t < tfinal +
+
+Equation + +
+EW(t) = CW mW (TW(t)−Tinit) +
+
+Description + +
    +
  • +EW is the change in heat energy in the water (J) +
    • +
  • +t is the time (s) +
    • +
  • +CW is the specific heat capacity of water (J/(kg⋅°C)) +
    • +
  • +mW is the mass of water (kg) +
    • +
  • +TW is the temperature of the water (°C) +
    • +
  • +Tinit is the initial temperature (°C) +
    • +
+
+Notes + +

+The above equation is derived using TM: sensHtE. EW is the change in thermal energy of the liquid water relative to the energy at the initial temperature (Tinit) (J). CW is the specific heat capacity of liquid water (J/(kg⋅°C)) and mW is the mass of the water (kg). The change in temperature is the difference between the temperature at time t (s), TW and the initial temperature, Tinit (°C). This equation applies as long as 0 < TW < 100°C (A: Water-Always-Liquid, A: Atmospheric-Pressure-Tank). +

+
+Source + +

+koothoor2013 +

+
+RefBy + +

+FR: Find-Mass FR: Calculate-Change-Heat_Energy-Water-Over-Time. +

+
+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Label + +

+Heat energy in the PCM +

+
+Input + +

+TmeltP, tfinal, Tinit, AP, hP, mP, CPS, CPL, TP, Hf, tmeltinit +

+
+Output + +

+EP +

+
+Input Constraints + +
+Tinit < TmeltP +
+
+Output Constraints + +
+0 < t < tfinal +
+
+Equation + +
+EP = +{ + +
+ +CPS mP (TP(t)−Tinit) , +TP < TmeltP + + + +EPmeltinit+Hf mP+CPL mP (TP(t)−TmeltP) , +TP > TmeltP + + + +EPmeltinit+QP(t) , +TP = TmeltP + + + +EPmeltinit+QP(t) , +0 < ϕ < 1 + + +
 +
+
+Description + +
    +
  • +EP is the change in heat energy in the PCM (J) +
    • +
  • +CPS is the specific heat capacity of PCM as a solid (J/(kg⋅°C)) +
    • +
  • +mP is the mass of phase change material (kg) +
    • +
  • +TP is the temperature of the phase change material (°C) +
    • +
  • +t is the time (s) +
    • +
  • +Tinit is the initial temperature (°C) +
    • +
  • +EPmeltinit is the change in heat energy in the PCM at the instant when melting begins (J) +
    • +
  • +Hf is the specific latent heat of fusion (J/kg) +
    • +
  • +CPL is the specific heat capacity of PCM as a liquid (J/(kg⋅°C)) +
    • +
  • +TmeltP is the melting point temperature for PCM (°C) +
    • +
  • +QP is the latent heat energy added to PCM (J) +
    • +
  • +ϕ is the melt fraction (Unitless) +
    • +
+
+Notes + +

+The above equation is derived using TM: sensHtE and TM: latentHtE. EP is the change in thermal energy of the PCM relative to the energy at the initial temperature (Tinit) J. EP for the solid PCM is found using TM: sensHtE for sensible heat ing, with the specific heat capacity of the solid PCM, CPS (J/(kg⋅°C)) and the change in the PCM temperature from the initial temperature (°C). EP for the melted PCM (TP > EPmeltinit) is found using TM: sensHtE for sensible heat of the liquid. PCM plus the energy when melting starts, plus the energy required to melt all of the PCM The energy when melting starts is EPmeltinit (J). The energy required to melt all of the PCM is Hf mP (J) (DD: htFusion). the specific heat capacity of the liquid PCM is CPL (J/(kg⋅°C)) and the change in temperature is TP−TmeltP (°C). EP during melting of the PCM is found using the energy required at the instant melting of the PCM begins, EPmeltinit plus the latent heat energy added to the PCM, QP (J) since the time when melting began tmeltinit (s). The heat energy for boiling of the PCM is not detailed, since the PCM is assumed to either be in a solid or liquid state (A: No-Gaseous-State-PCM) (A: PCM-Initially-Solid). +

+
+Source + +

+koothoor2013 +

+
+RefBy + +

+UC: No-Gaseous-State FR: Find-Mass IM: eBalanceOnPCM FR: Calculate-Change-Heat_Energy-PCM-Over-Time. +

+
+
+
+
+
+
+

+Data Constraints +

+

+Table:InDataConstraints and Table:OutDataConstraints show the data constraints on the input and output variables, respectively. The column for physical constraints gives the physical limitations on the range of values that can be taken by the variable. The uncertainty column provides an estimate of the confidence with which the physical quantities can be measured. This information would be part of the input if one were performing an uncertainty quantification exercise. The constraints are conservative, to give the user of the model the flexibility to experiment with unusual situations. The column of typical values is intended to provide a feel for a common scenario. The column for software constraints restricts the range of inputs to reasonable values.(*) These quantities cannot be equal to zero, or there will be a divide by zero in the model. (+) These quantities cannot be zero, or there would be freezing (A: PCM-Initially-Solid). (++) The constraints on the surface area are calculated by considering the surface area to volume ratio. The assumption is that the lowest ratio is 1 and the highest possible is

+ +2 + + +hmin + +
, where hmin is the thickness of a "sheet" of PCM. A thin sheet has the greatest surface area to volume ratio. (**) The constraint on the maximum time at the end of the simulation is the total number of seconds in one day. +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Var + +Physical Constraints + +Software Constraints + +Typical Value + +Uncert. +
+AC + +AC > 0 + +AC ≤ ACmax + +120.0⋅10-3 m2 + +10.0% +
+AP + +AP > 0 + +VP ≤ AP ≤ 
+ +2 + + +hmin + +
 Vtank +		 +1.2 m2 + +10.0% +
+CW + +CW > 0 + +CWmin < CW < CWmax + +4.186⋅103 J/(kg⋅°C) + +10.0% +
+CPL + +CPL > 0 + +CPLmin < CPL < CPLmax + +2.27⋅103 J/(kg⋅°C) + +10.0% +
+CPS + +CPS > 0 + +CPSmin < CPS < CPSmax + +1.76⋅103 J/(kg⋅°C) + +10.0% +
+D + +D > 0 + +-- + +412.0⋅10-3 m + +10.0% +
+hC + +hC > 0 + +hCmin ≤ hC ≤ hCmax + +1.0⋅103 W/(m2⋅°C) + +10.0% +
+Hf + +Hf > 0 + +Hfmin < Hf < Hfmax + +211.6⋅103 J/kg + +10.0% +
+hP + +hP > 0 + +hPmin ≤ hP ≤ hPmax + +1.0⋅103 W/(m2⋅°C) + +10.0% +
+L + +L > 0 + +Lmin ≤ L ≤ Lmax + +1.5 m + +10.0% +
+TC + +0 < TC < 100 + +-- + +50.0 °C + +10.0% +
+tfinal + +tfinal > 0 + +tfinal < tfinalmax + +50.0⋅103 s + +10.0% +
+Tinit + +0 < Tinit < Tmelt + +-- + +40.0 °C + +10.0% +
+TmeltP + +0 < TmeltP < TC + +-- + +44.2 °C + +10.0% +
+VP + +0 < VP < Vtank + +VP ≥ MINFRACT Vtank + +500.0⋅10-3 m3 + +10.0% +
+ρP + +ρPmin < ρP < ρPmax + +-- + +1.007⋅103 kg/m3 + +10.0% +
+ρW + +ρW > 0 + +ρWmin < ρW ≤ ρWmax + +1.0⋅103 kg/m3 + +10.0% +
+

+Input Data Constraints +

+
+
+ + + + + + + + + + + + + + + + + + + + + +
+Var + +Physical Constraints +
+TW + +Tinit ≤ TW ≤ TC +
+TP + +Tinit ≤ TP ≤ TC +
+EW + +EW ≥ 0 +
+EP + +EP ≥ 0 +
+

+Output Data Constraints +

+
+
+
+
+
+

+Properties of a Correct Solution +

+

+A correct solution must exhibit the law of conservation of energy. This means that the change in heat energy in the water should equal the difference between the total energy input from the heating coil and the energy output to the PCM. This can be shown as an equation by taking DD: ht_flux_C and DD: ht_flux_P, multiplying each by their respective surface area of heat transfer, and integrating each over the simulation time, as follows: +

+
+EW = ∫0thC AC (TC−TW(t)) dt−∫0thP AP (TW(t)−TP(t)) dt +
+

+In addition, the change in heat energy in the PCM should equal the energy input to the PCM from the water. This can be expressed as +

+
+EP = ∫0thP AP (TW(t)−TP(t)) dt +
+

+Equations (FIXME: Equation 7) and (FIXME: Equation 8) can be used as "sanity" checks to gain confidence in any solution computed by SWHS. The relative error between the results computed by SWHS and the results calculated from the RHS of these equations should be less than 0.001% FR: Verify-Energy-Output-Follow-Conservation-of-Energy. +

+
+
+
+
+
+
+
+
+

+Requirements +

+

+This section provides the functional requirements, the business tasks that the software is expected to complete, and the non-functional requirements, the qualities that the software is expected to exhibit. +

+
+
+

+Functional Requirements +

+
+

+

+Input-Initial-Quantities: Input the following quantities described in Table:Input-Variable-Requirements, which define the tank parameters, material properties and initial conditions. A: Volume-Coil-Negligible. +
+

+

+

+Find-Mass: Use the inputs in FR: Input-Initial-Quantities to find the mass needed for IM: eBalanceOnWtr, IM: eBalanceOnPCM, IM: heatEInWtr, and IM: heatEInPCM, using mW = VW ρW = (Vtank−VP) ρW = (
+ +D + + +2 + +
 L−VP) ρW and mP = VP ρP, where VW is the volume of water and Vtank is the volume of the cylindrical tank. +
+

+

+

+Check-Input-with-Physical_Constraints: Verify that the inputs satisfy the required physical constraints. +
+

+

+

+Output-Input-Derived-Quantities: Output the input quantities and derived quantities in the following list: the quantities from FR: Input-Initial-Quantities, the masses from FR: Find-Mass, τW (from IM: eBalanceOnWtr), η (from IM: eBalanceOnWtr), τPS (from IM: eBalanceOnPCM) and τPL (from IM: eBalanceOnPCM). +
+

+

+

+Calculate-Temperature-Water-Over-Time: Calculate and output the temperature of the water (TW(t)) over the simulation time (from IM: eBalanceOnWtr). +
+

+

+

+Calculate-Temperature-PCM-Over-Time: Calculate and output the temperature of the phase change material (TP(t)) over the simulation time (from IM: eBalanceOnPCM). +
+

+

+

+Calculate-Change-Heat_Energy-Water-Over-Time: Calculate and output the change in heat energy in the water (EW(t)) over the simulation time (from IM: heatEInWtr). +
+

+

+

+Calculate-Change-Heat_Energy-PCM-Over-Time: Calculate and output the change in heat energy in the PCM (EP(t)) over the simulation time (from IM: heatEInPCM). +
+

+

+

+Verify-Energy-Output-Follow-Conservation-of-Energy: Verify that the energy outputs (EW(t) and EP(t)) follow the law of conservation of energy with relative error no greater than 0.001%. +
+

+

+

+Calculate-PCM-Melt-Begin-Time: Calculate and output the time at which the PCM begins to melt tmeltinit (from IM: eBalanceOnPCM). +
+

+

+

+Calculate-PCM-Melt-End-Time: Calculate and output the time at which the PCM stops melting tmeltfinal (from IM: eBalanceOnPCM). +
+

+
+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Symbol + +Unit + +Description +
+L + +m + +length of tank +
+D + +m + +diameter of tank +
+VP + +m3 + +volume of PCM +
+AP + +m2 + +phase change material surface area +
+ρP + +kg/m3 + +density of PCM +
+TmeltP + +°C + +melting point temperature for PCM +
+CPS + +J/(kg⋅°C) + +specific heat capacity of PCM as a solid +
+CPL + +J/(kg⋅°C) + +specific heat capacity of PCM as a liquid +
+Hf + +J/kg + +specific latent heat of fusion +
+AC + +m2 + +heating coil surface area +
+TC + +°C + +temperature of the heating coil +
+ρW + +kg/m3 + +density of water +
+CW + +J/(kg⋅°C) + +specific heat capacity of water +
+hC + +W/(m2⋅°C) + +convective heat transfer coefficient between coil and water +
+hP + +W/(m2⋅°C) + +convective heat transfer coefficient between PCM and water +
+Tinit + +°C + +initial temperature +
+tfinal + +s + +final time +
+

+Input Variable Requirements +

+
+
+
+
+
+

+Non-Functional Requirements +

+

+This problem is small in size and relatively simple, so performance is not a priority. Any reasonable implementation will be very quick and use minimal storage. Rather than performance, the non-functional requirement priorities are correctness, verifiability, understandability, reusability, and maintainability. +

+
+
+
+
+
+
+

+Likely Changes +

+
+

+

+Uniform-Temperature-PCM: A: Temp-PCM-Constant-Across-Volume - PCM is actually a poor thermal conductor, so the assumption of uniform temperature of the phase change material is not likely. +
+

+

+

+Temperature-Coil-Variable-Over-Day: A: Temp-Heating-Coil-Constant-over-Time - The temperature of the heating coil will change over the course of the day, depending on the energy received from the sun. +
+

+

+

+Temperature-Coil-Variable-Over-Length: A: Temp-Heating-Coil-Constant-over-Length - The temperature of the heating coil will actually change along its length as the water within it cools. +
+

+

+

+Discharging-Tank: A: Charging-Tank-No-Temp-Discharge - The model currently only accounts for charging of the tank. A more complete model would also account for discharging of the tank. +
+

+

+

+Different-Initial-Temps-PCM-Water: A: Same-Initial-Temp-Water-PCM - To add more flexibility to the simulation, the initial temperature of the water and the PCM could be allowed to have different values. +
+

+

+

+Tank-Lose-Heat: A: Perfect-Insulation-Tank - Any real tank cannot be perfectly insulated and will lose heat. +
+

+
+
+
+
+
+

+Unlikely Changes +

+
+

+

+Water-PCM-Fixed-States: A: Water-Always-Liquid , A: No-Gaseous-State-PCM - It is unlikely for the change of water from liquid to a solid or the state change of the phase change material from a liquid to a gas to be considered. +
+

+

+

+No-Internal-Heat-Generation: A: No-Internal-Heat-Generation-By-Water-PCM - Is used for the derivations of IM: eBalanceOnWtr and IM: eBalanceOnPCM. +
+

+

+

+No-Gaseous-State: A: No-Gaseous-State-PCM - Is used for the derivation of IM: eBalanceOnPCM and for the equation given by IM: heatEInPCM to be valid. +
+

+
+
+
+
+
+

+Traceability Matrices and Graphs +

+

+The purpose of the traceability matrices is to provide easy references on what has to be additionally modified if a certain component is changed. Every time a component is changed, the items in the row of that component that are marked with an "X" should be modified as well. Table:Tracey shows the dependencies of theoretical models, general definitions, data definitions, and instance models with each other. Table:Tracey2 shows the dependencies of instance models, requirements, and data constraints on each other. Table:Tracey1 shows the dependencies of theoretical models, general definitions, data definitions, instance models, and likely changes on the assumptions. +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ + +FR: Input-Initial-Quantities + +IM: heatEInWtr + +IM: eBalanceOnWtr + +LC: Discharging-Tank + +GD: rocTempSimp + +DD: ht_flux_P + +GD: nwtnCooling + +DD: ht_flux_C + +UC: Water-PCM-Fixed-States + +UC: No-Gaseous-State + +IM: heatEInPCM + +IM: eBalanceOnPCM + +UC: No-Internal-Heat-Generation + +LC: Tank-Lose-Heat + +LC: Different-Initial-Temps-PCM-Water + +A: Charging-Tank-No-Temp-Discharge + +TM: consThermE + +LC: Temperature-Coil-Variable-Over-Length + +LC: Temperature-Coil-Variable-Over-Day + +LC: Uniform-Temperature-PCM + +FR: Output-Input-Derived-Quantities + +FR: Find-Mass + +FR: Calculate-Temperature-PCM-Over-Time + +FR: Calculate-PCM-Melt-End-Time + +FR: Calculate-PCM-Melt-Begin-Time + +FR: Calculate-Temperature-Water-Over-Time + +FR: Calculate-Change-Heat_Energy-PCM-Over-Time + +FR: Calculate-Change-Heat_Energy-Water-Over-Time + +DD: melt_frac + +TM: latentHtE + +TM: sensHtE +
+Table:Input-Variable-Requirements + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+A: Charging-Tank-No-Temp-Discharge + + + + + +X + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+A: Constant-Water-Temp-Across-Tank + + + + + + + + + +X + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+A: Density-Water-PCM-Constant-over-Volume + + + + + + + + + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+A: Newton-Law-Convective-Cooling-Coil-Water + + + + + + + + + + + + + + + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+A: Law-Convective-Cooling-Water-PCM + + + + + + + + + + + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+A: No-Gaseous-State-PCM + + + + + + + + + + + + + + + + + +X + +X + +X + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+A: No-Internal-Heat-Generation-By-Water-PCM + + + + + +X + + + + + + + + + + + + + + + + + +X + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+A: Specific-Heat-Energy-Constant-over-Volume + + + + + + + + + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+A: Temp-Heating-Coil-Constant-over-Time + + + + + + + + + + + + + + + +X + + + + + + + + + + + + + + + + + + + + + +X + + + + + + + + + + + + + + + + + + + + + + + + +
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+A: Volume-Change-Melting-PCM-Negligible + + + + + + + + + + + + + + + + + + + + + + + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+A: Volume-Coil-Negligible + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+

+Traceability Matrix Showing the Connections Between Items of Different Sections +

+
+
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+IM4 (IM: heatEInPCM) + + + +X + +X + + + + + + + +X + +X + +X + + + +X + + + + +
+

+Traceability Matrix Showing the Connections Between Items of Different Sections +

+
+
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+IM1 (IM: eBalanceOnWtr) + + + +X + + + + + + + +X + +X + + + + + + + + + + + + + + + + + + +
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+

+Traceability Matrix Showing the Connections Between Requirements and Instance Models +

+
+
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+ + +A1 (A: Thermal-Energy-Only) + +A2 (A: Heat-Transfer-Coeffs-Constant) + +A3 (A: Constant-Water-Temp-Across-Tank) + +A4 (A: Temp-PCM-Constant-Across-Volume) + +A5 (A: Density-Water-PCM-Constant-over-Volume) + +A6 (A: Specific-Heat-Energy-Constant-over-Volume) + +A7 (A: Newton-Law-Convective-Cooling-Coil-Water) + +A8 (A: Temp-Heating-Coil-Constant-over-Time) + +A9 (A: Temp-Heating-Coil-Constant-over-Length) + +A10 (A: Law-Convective-Cooling-Water-PCM) + +A11 (A: Charging-Tank-No-Temp-Discharge) + +A12 (A: Same-Initial-Temp-Water-PCM) + +A13 (A: PCM-Initially-Solid) + +A14 (A: Water-Always-Liquid) + +A15 (A: Perfect-Insulation-Tank) + +A16 (A: No-Internal-Heat-Generation-By-Water-PCM) + +A17 (A: Volume-Change-Melting-PCM-Negligible) + +A18 (A: No-Gaseous-State-PCM) + +A19 (A: Atmospheric-Pressure-Tank) +
+T1 (TM: consThermE) + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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+IM4 (IM: heatEInPCM) + + + + + + + + + + + + + + + + + + + + + + + + + +X + + + + + + + + + +X + + +
+LC1 (LC: Uniform-Temperature-PCM) + + + + + + + +X + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+LC2 (LC: Temperature-Coil-Variable-Over-Day) + + + + + + + + + + + + + + + +X + + + + + + + + + + + + + + + + + + + + + + +
+LC3 (LC: Temperature-Coil-Variable-Over-Length) + + + + + + + + + + + + + + + + + +X + + + + + + + + + + + + + + + + + + + + +
+LC4 (LC: Discharging-Tank) + + + + + + + + + + + + + + + + + + + + + +X + + + + + + + + + + + + + + + + +
+LC5 (LC: Different-Initial-Temps-PCM-Water) + + + + + + + + + + + + + + + + + + + + + + + +X + + + + + + + + + + + + + + +
+LC6 (LC: Tank-Lose-Heat) + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +X + + + + + + + + +
+

+Traceability Matrix Showing the Connections Between Assumptions and Other Items +

+
+

+The purpose of the traceability graphs is also to provide easy references on what has to be additionally modified if a certain component is changed. The arrows in the graphs represent dependencies. The component at the tail of an arrow is depended on by the component at the head of that arrow. Therefore, if a component is changed, the components that it points to should also be changed. Fig:TraceyA shows the dependencies of theoretical models, general definitions, data definitions, instance models, likely changes, and assumptions on each other. Fig:TraceyR shows the dependencies of instance models, requirements, and data constraints on each other. +

+
+
+Traceability Graph Showing the Connections Between Items of Different Sections +
+Traceability Graph Showing the Connections Between Items of Different Sections +
+
+
+
+
+Traceability Graph Showing the Connections Between Instance Models, Requirements, and Data Constraints +
+Traceability Graph Showing the Connections Between Instance Models, Requirements, and Data Constraints +
+
+
+
+
+
+
+

+Values of Auxiliary Constants +

+

+This section contains the standard values that are used for calculations in SWHS. +

+
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Symbol + +Description + +Value + +Unit +
+CWmax + +maximum specific heat capacity of water + +4210 + +J/(kg⋅°C) +
+CWmin + +minimum specific heat capacity of water + +4170 + +J/(kg⋅°C) +
+CPLmax + +maximum specific heat capacity of PCM as a liquid + +5000 + +J/(kg⋅°C) +
+CPLmin + +minimum specific heat capacity of PCM as a liquid + +100 + +J/(kg⋅°C) +
+CPSmax + +maximum specific heat capacity of PCM as a solid + +4000 + +J/(kg⋅°C) +
+CPSmin + +minimum specific heat capacity of PCM as a solid + +100 + +J/(kg⋅°C) +
+hCmax + +maximum convective heat transfer coefficient between coil and water + +10000 + +W/(m2⋅°C) +
+hCmin + +minimum convective heat transfer coefficient between coil and water + +10 + +W/(m2⋅°C) +
+hPmax + +maximum convective heat transfer coefficient between PCM and water + +10000 + +W/(m2⋅°C) +
+hPmin + +minimum convective heat transfer coefficient between PCM and water + +10 + +W/(m2⋅°C) +
+Lmax + +maximum length of tank + +50 + +m +
+Lmin + +minimum length of tank + +100.0⋅10-3 + +m +
+MINFRACT + +minimum fraction of the tank volume taken up by the PCM + +1.0⋅10-6 + +-- +
+tfinalmax + +maximum final time + +86400 + +s +
+ρPmax + +maximum density of PCM + +20000 + +kg/m3 +
+ρPmin + +minimum density of PCM + +500 + +kg/m3 +
+ρWmax + +maximum density of water + +1000 + +kg/m3 +
+ρWmin + +minimum density of water + +950 + +kg/m3 +
+

+Auxiliary Constants +

+
+
+
+
+
+

+References +

+
    +
  • +
    +[1]: Bueche, J. Frederick. Introduction to Physics for Scientists. 4nd. ed., New York City, New York: McGraw Hill, 1986. Print. +
    +
    • +
  • +
    +[2]: Incropera, F. P., Dewitt, D. P., Bergman, T. L., and Lavine, A. S. Fundamentals of Heat and Mass Transfer. 6th. ed., Hoboken, New Jersey: John Wiley and Sons, 2007. Print. +
    +
    • +
  • +
    +[3]: Koothoor, Nirmitha. A document drive approach to certifying scientific computing software. McMaster University, Hamilton, ON, Canada: 2013. Print. +
    +
    • +
  • +
    +[4]: Lightstone, Marilyn. Derivation of tank/pcm model. 2012. From Marilyn Lightstone's Personal Notes +
    +
    • +
  • +
    +[5]: Parnas, David L. "On the Criteria To Be Used in Decomposing Systems into Modules." Communications of the ACM, 1972. pp. 1053–1058. Print. +
    +
    • +
  • +
    +[6]: Parnas, David L. and Clements, P. C. "A rational design process: How and why to fake it." IEEE Transactions on Software Engineering, vol. 12, no. 2, Washington, USA: February, 1986. pp. 251–257. Print. +
    +
    • +
  • +
    +[7]: Parnas, David L., Clements, P. C., and Wiess. "The Modular Structure of Complex Systems." ICSE '84: Proceedings of the 7th international conference on Software engineering. 1984. pp. 408–417. +
    +
    • +
  • +
    +[8]: Smith, W. Spencer and Lai, Lei. "A new requirements template for scientific computing." Proceedings of the First International Workshop on Situational Requirements Engineering Processes - Methods, Techniques and Tools to Support Situation-Specific Requirements Engineering Processes, SREP'05. Edited by PJ Agerfalk, N. Kraiem, and J. Ralyte, Paris, France: 2005. pp. 107–121. In conjunction with 13th IEEE International Requirements Engineering Conference, +
    +
    • +
+
+
+ + diff --git a/code/drasil-example/Drasil/SWHS/DataDefs.hs b/code/drasil-example/Drasil/SWHS/DataDefs.hs index 8e23c7f945..3b09a4a4a2 100644 --- a/code/drasil-example/Drasil/SWHS/DataDefs.hs +++ b/code/drasil-example/Drasil/SWHS/DataDefs.hs @@ -6,9 +6,10 @@ import Drasil.DocLang (ModelDB, mdb) import Drasil.SWHS.Assumptions (assumpCWTAT, assumpTPCAV, assumpLCCCW, assumpTHCCoT, assumpTHCCoL, assumpLCCWP) -import Drasil.SWHS.References (bueche1986, koothoor2013) +import Drasil.SWHS.References (bueche1986, koothoor2013, lightstone2012) import Drasil.SWHS.Unitals (melt_frac, latentE_P, htFusion, pcm_mass, - temp_W, temp_PCM, ht_flux_P, pcm_HTC, coil_HTC, temp_C, ht_flux_C) + temp_W, temp_PCM, ht_flux_P, pcm_HTC, coil_HTC, temp_C, ht_flux_C, htCap_S_P, + pcm_HTC, pcm_SA, tau_S_P) import Data.Drasil.Quantities.Physics (time) import Data.Drasil.Quantities.PhysicalProperties (mass) @@ -18,10 +19,12 @@ swhsRefMDB :: ModelDB swhsRefMDB = mdb [] [] swhsDDefs [] swhsQDefs :: [QDefinition] -swhsQDefs = [dd1HtFluxCQD, dd2HtFluxPQD, dd3HtFusionQD, dd4MeltFracQD] +swhsQDefs = [dd1HtFluxCQD, dd2HtFluxPQD, ddBalanceSolidPCMQD, dd3HtFusionQD, + dd4MeltFracQD] swhsDDefs :: [DataDefinition] -swhsDDefs = [dd1HtFluxC, dd2HtFluxP, dd3HtFusion, dd4MeltFrac] +swhsDDefs = [dd1HtFluxC, dd2HtFluxP, ddBalanceSolidPCM, dd3HtFusion, + dd4MeltFrac] -- FIXME? This section looks strange. Some data defs are created using -- terms, some using defns, and some with a brand new description. @@ -34,7 +37,8 @@ htFluxCEqn :: Expr htFluxCEqn = (sy coil_HTC) * ((sy temp_C) - apply1 temp_W time) dd1HtFluxC :: DataDefinition -dd1HtFluxC = mkDD dd1HtFluxCQD [koothoor2013] [] "ht_flux_C" [makeRef2S assumpLCCCW, makeRef2S assumpTHCCoT, makeRef2S assumpTHCCoL] +dd1HtFluxC = mkDD dd1HtFluxCQD [koothoor2013] [] "ht_flux_C" + [makeRef2S assumpLCCCW, makeRef2S assumpTHCCoT, makeRef2S assumpTHCCoL] --Can't include info in description beyond definition of variables? ---- @@ -46,7 +50,21 @@ htFluxPEqn :: Expr htFluxPEqn = (sy pcm_HTC) * (apply1 temp_W time - apply1 temp_PCM time) dd2HtFluxP :: DataDefinition -dd2HtFluxP = mkDD dd2HtFluxPQD [koothoor2013] [] "ht_flux_P" [makeRef2S assumpCWTAT, makeRef2S assumpTPCAV, makeRef2S assumpLCCWP] +dd2HtFluxP = mkDD dd2HtFluxPQD [koothoor2013] [] "ht_flux_P" + [makeRef2S assumpCWTAT, makeRef2S assumpTPCAV, makeRef2S assumpLCCWP] + +---- + +ddBalanceSolidPCMQD :: QDefinition +ddBalanceSolidPCMQD = mkQuantDef tau_S_P balanceSolidPCMEqn + +balanceSolidPCMEqn :: Expr +balanceSolidPCMEqn = ((sy pcm_mass) * (sy htCap_S_P)) / + ((sy pcm_HTC) * (sy pcm_SA)) + +ddBalanceSolidPCM :: DataDefinition +ddBalanceSolidPCM = mkDD ddBalanceSolidPCMQD [lightstone2012] [] + "BalanceSolidPCM" [] ---- @@ -58,7 +76,7 @@ htFusionEqn = (sy latent_heat) / (sy mass) -- FIXME: need to allow page references in references. dd3HtFusion :: DataDefinition -dd3HtFusion = mkDD dd3HtFusionQD [bueche1986 {- +:+ sParen (S "pg. 282") -} ] +dd3HtFusion = mkDD dd3HtFusionQD [bueche1986 {- +:+ sParen (S "pg. 282") -} ] [] "htFusion" [] ---- diff --git a/code/drasil-example/Drasil/SWHS/IMods.hs b/code/drasil-example/Drasil/SWHS/IMods.hs index 36e14b6660..16af26a26f 100644 --- a/code/drasil-example/Drasil/SWHS/IMods.hs +++ b/code/drasil-example/Drasil/SWHS/IMods.hs @@ -13,7 +13,8 @@ import Data.Drasil.Concepts.Thermodynamics (boil_pt, boiling, heat, heat_cap_spe import Drasil.SWHS.Assumptions (assumpCTNOD, assumpSITWP, assumpPIS, assumpWAL, assumpPIT, assumpNIHGBWP, assumpVCMPN, assumpNGSP, assumpAPT) import Drasil.SWHS.Concepts (coil, phsChgMtrl, tank, water) -import Drasil.SWHS.DataDefs (dd1HtFluxC, dd2HtFluxP, dd3HtFusion, dd4MeltFrac) +import Drasil.SWHS.DataDefs (dd1HtFluxC, dd2HtFluxP, dd3HtFusion, dd4MeltFrac, + ddBalanceSolidPCM) import Drasil.SWHS.References (koothoor2013) import Drasil.SWHS.TMods (sensHtE, latentHtE) import Drasil.SWHS.Unitals (coil_HTC, coil_SA, eta, ht_flux_C, ht_flux_P, htCap_L_P, @@ -223,8 +224,9 @@ balPCMDesc = foldlSent [(E $ sy temp_W) `isThe` phrase temp_W +:+. sParen (unwrap $ getUnit temp_W), (E $ sy temp_PCM) `isThe` phrase temp_PCM +:+. sParen (unwrap $ getUnit temp_PCM), (E $ (sy tau_S_P) $= ((sy pcm_mass) * (sy htCap_S_P)) / - ((sy pcm_HTC) * (sy pcm_SA))), S "is a constant" +:+. - sParen (unwrap $ getUnit tau_S_P), (E $ (sy tau_L_P) $= + ((sy pcm_HTC) * (sy pcm_SA))), S "is a constant" +:+ + sParen (unwrap $ getUnit tau_S_P) +:+. + sParen (makeRef2S ddBalanceSolidPCM), (E $ (sy tau_L_P) $= ((sy pcm_mass) * (sy htCap_L_P)) / ((sy pcm_HTC) * (sy pcm_SA))), S "is a constant", sParen (unwrap $ getUnit tau_S_P)] @@ -239,7 +241,7 @@ balPCMDesc_note = foldlSent [ (S "with initial conditions") `sC` (E $ (sy temp_W $= sy temp_PCM $= sy temp_init)) `sC` (S "FIXME t_w(0) = t_p(0)") `sC` makeRef2S assumpSITWP `sC` (S "and"), (E $ (sy temp_W)), - S "from IM1, such that the following governing ODE is satisfied.", + S "from", (makeRef2S eBalanceOnWtr) `sC` S "such that the following governing ODE is satisfied.", S "The temperature remains constant at", (E $ (sy temp_melt_P)) `sC` (S "even with the heating (or cool-ing), until the phase change has occurred for all of the material; that is as long as"), diff --git a/code/stable/glassbr/SRS/GlassBR_SRS-blx.bib b/code/stable/glassbr/SRS/GlassBR_SRS-blx.bib new file mode 100644 index 0000000000..8aa2223224 --- /dev/null +++ b/code/stable/glassbr/SRS/GlassBR_SRS-blx.bib @@ -0,0 +1,11 @@ +@Comment{$ biblatex control file $} +@Comment{$ biblatex version 2.7 $} +Do not modify this file! + +This is an auxiliary file used by the 'biblatex' package. +This file may safely be deleted. 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e_i`Ma3>}=@KIah-I9a$kSve3WDaGW)5&jp+?1qQ{ literal 0 HcmV?d00001 diff --git a/code/stable/glassbr/SRS/GlassBR_SRS.run.xml b/code/stable/glassbr/SRS/GlassBR_SRS.run.xml new file mode 100644 index 0000000000..059045f3b0 --- /dev/null +++ b/code/stable/glassbr/SRS/GlassBR_SRS.run.xml @@ -0,0 +1,92 @@ + + + + + + + + + + + + + + + + + + + + + + + + +]> + + + latex + + GlassBR_SRS.aux + GlassBR_SRS-blx.bib + + + GlassBR_SRS.bbl + + + blx-dm.def + blx-compat.def + blx-bibtex.def + biblatex.def + numeric.bbx + standard.bbx + numeric.cbx + biblatex.cfg + english.lbx + + + + bibtex + + bibtex + + GlassBR_SRS + + + GlassBR_SRS.aux + + + GlassBR_SRS.bbl + + + GlassBR_SRS.bbl + + + GlassBR_SRS.aux + GlassBR_SRS-blx.bib + + + bibfile.bib + + + biblatex.bst + + + diff --git a/code/stable/glassbr/SRS/bibfile.bib b/code/stable/glassbr/SRS/bibfile.bib new file mode 100644 index 0000000000..8df4a1e23b --- /dev/null +++ b/code/stable/glassbr/SRS/bibfile.bib @@ -0,0 +1,69 @@ +@misc{astm2009, +author={ASTM}, +title={Standard Practice for Determining Load Resistance of Glass in Buildings}, +publisher={ASTM International}, +booktitle={Standard E1300-09a}, +year={2009}, +howpublished={\url{www.astm.org}}} + +@misc{astm2012, +author={ASTM}, +title={Standard Specification for Heat-Strengthened and Fully Tempered Flat Glass}, +publisher={ASTM International}, +address={West Conshohocken, PA}, +year={2012}, +howpublished={\url{https://doi.org/10.1520/C1048-12E01}}} + +@misc{astm2016, +author={ASTM}, +title={Standard specification for Flat Glass}, +publisher={ASTM International}, +address={West Conshohocken, PA}, +year={2016}, +howpublished={\url{https://doi.org/10.1520/C1036-16}}} + +@misc{beasonEtAl1998, +author={Beason, W. Lynn and Kohutek, Terry L. and Bracci, Joseph M.}, +title={Basis for ASTME E 1300 Annealed Glass Thickness Selection Charts}, +booktitle={ASCE Library}, +month=feb, +year={1998}, +howpublished={\url{doi.org/10.1061/(ASCE)0733-9445(1998)124:2(215)}}} + +@booklet{campidelli, +title={Glass-BR Software for the design and risk assessment of glass facades subjected to blast loading}, +author={Campidelli, Manuel}} + +@mastersthesis{koothoor2013, +author={Koothoor, Nirmitha}, +title={A document drive approach to certifying scientific computing software}, +school={McMaster University}, +year={2013}, +address={Hamilton, ON, Canada}} + +@article{parnasClements1986, +author={Parnas, David L. and Clements, P. C.}, +title={A rational design process: How and why to fake it}, +journal={IEEE Transactions on Software Engineering}, +year={1986}, +month=feb, +volume={12}, +number={2}, +pages={"251-257"}, +address={Washington, USA}} + +@misc{rbrtsn2012, +author={Robertson, James and Robertson, Suzanne}, +title={Volere requirements specification template edition 16}, +howpublished={\url{https://pdfs.semanticscholar.org/cf57/27a59801086cbd3d14e587e09880561dbe22.pdf}}, +year={2012}} + +@inproceedings{smithLai2005, +author={Smith, W. Spencer and Lai, Lei}, +title={A new requirements template for scientific computing}, +booktitle={Proceedings of the First International Workshop on Situational Requirements Engineering Processes - Methods, Techniques and Tools to Support Situation-Specific Requirements Engineering Processes, SREP'05}, +year={2005}, +editor={Agerfalk, PJ and Kraiem, N. and Ralyte, J.}, +address={Paris, France}, +pages={"107-121"}, +note={In conjunction with 13th IEEE International Requirements Engineering Conference,}} diff --git a/code/stable/swhs/SRS/SWHS_SRS-blx.bib b/code/stable/swhs/SRS/SWHS_SRS-blx.bib new file mode 100644 index 0000000000..8aa2223224 --- /dev/null +++ b/code/stable/swhs/SRS/SWHS_SRS-blx.bib @@ -0,0 +1,11 @@ +@Comment{$ biblatex control file $} +@Comment{$ biblatex version 2.7 $} +Do not modify this file! + +This is an auxiliary file used by the 'biblatex' package. +This file may safely be deleted. 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a/code/stable/swhs/SRS/SWHS_SRS.run.xml b/code/stable/swhs/SRS/SWHS_SRS.run.xml new file mode 100644 index 0000000000..08423d6346 --- /dev/null +++ b/code/stable/swhs/SRS/SWHS_SRS.run.xml @@ -0,0 +1,92 @@ + + + + + + + + + + + + + + + + + + + + + + + + +]> + + + latex + + SWHS_SRS.aux + SWHS_SRS-blx.bib + + + SWHS_SRS.bbl + + + blx-dm.def + blx-compat.def + blx-bibtex.def + biblatex.def + numeric.bbx + standard.bbx + numeric.cbx + biblatex.cfg + english.lbx + + + + bibtex + + bibtex + + SWHS_SRS + + + SWHS_SRS.aux + + + SWHS_SRS.bbl + + + SWHS_SRS.bbl + + + SWHS_SRS.aux + SWHS_SRS-blx.bib + + + bibfile.bib + + + biblatex.bst + + + diff --git a/code/stable/swhs/SRS/SWHS_SRS.tex b/code/stable/swhs/SRS/SWHS_SRS.tex index 6c07adefdb..265d46f974 100644 --- a/code/stable/swhs/SRS/SWHS_SRS.tex +++ b/code/stable/swhs/SRS/SWHS_SRS.tex @@ -616,6 +616,37 @@ \subsubsection{Data Definitions} \end{minipage} \par~ +\noindent \begin{minipage}{\textwidth} +\begin{tabular}{p{0.2\textwidth} p{0.73\textwidth}} +\toprule \textbf{Refname} & \textbf{DD:BalanceSolidPCM} +\phantomsection +\label{DD:BalanceSolidPCM} +\\ \midrule \\ +Label & ODE parameter for solid PCM + \\ \midrule \\ + Symbol & ${{τ_{P}}^{S}}$ + \\ \midrule \\ + Units & s + \\ \midrule \\ + Equation & \begin{displaymath} + {{τ_{P}}^{S}}=\frac{{m_{P}} {{C_{P}}^{S}}}{{h_{P}} {A_{P}}} + \end{displaymath} + \\ \midrule \\ + Description & \begin{symbDescription} + \item{${{τ_{P}}^{S}}$ is the ODE parameter for solid PCM (s)} + \item{${m_{P}}$ is the mass of phase change material (kg)} + \item{${{C_{P}}^{S}}$ is the specific heat capacity of PCM as a solid ($\frac{\text{J}}{(\text{kg}{}^{\circ}\text{C})}$)} + \item{${h_{P}}$ is the convective heat transfer coefficient between PCM and water ($\frac{\text{W}}{(\text{m}^{2}{}^{\circ}\text{C})}$)} + \item{${A_{P}}$ is the phase change material surface area ($\text{m}^{2}$)} + \end{symbDescription} + \\ \midrule \\ + Source & \cite{lightstone2012} + \\ \midrule \\ + RefBy & \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM} +\\ \bottomrule \end{tabular} +\end{minipage} +\par~ + \noindent \begin{minipage}{\textwidth} \begin{tabular}{p{0.2\textwidth} p{0.73\textwidth}} \toprule \textbf{Refname} & \textbf{DD:htFusion} @@ -623,7 +654,7 @@ \subsubsection{Data Definitions} \label{DD:htFusion} \\ \midrule \\ Label & Specific latent heat of fusion - \\ \midrule \\ + \\ \midrule \\ Symbol & ${H_{f}}$ \\ \midrule \\ Units & $\frac{\text{J}}{\text{kg}}$ @@ -717,7 +748,7 @@ \subsubsection{Instance Models} \\ \midrule \\ Source & \cite{koothoor2013} \\ \midrule \\ - RefBy & \hyperref[unlikeChgNIHG]{UC: No-Internal-Heat-Generation} \hyperref[outputInputDerivQuants]{FR: Output-Input-Derived-Quantities} \hyperref[outputInputDerivQuants]{FR: Output-Input-Derived-Quantities} \hyperref[findMass]{FR: Find-Mass} \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr} \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM} \hyperref[calcTempWtrOverTime]{FR: Calculate-Temperature-Water-Over-Time}. + RefBy & \hyperref[unlikeChgNIHG]{UC: No-Internal-Heat-Generation} \hyperref[outputInputDerivQuants]{FR: Output-Input-Derived-Quantities} \hyperref[outputInputDerivQuants]{FR: Output-Input-Derived-Quantities} \hyperref[findMass]{FR: Find-Mass} \hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr} \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM} \hyperref[IM:eBalanceOnPCM]{IM: eBalanceOnPCM} \hyperref[calcTempWtrOverTime]{FR: Calculate-Temperature-Water-Over-Time}. \\ \bottomrule \end{tabular} \end{minipage} Derivation of the energy balance on water: @@ -790,7 +821,7 @@ \subsubsection{Instance Models} \item{$ϕ$ is the melt fraction (Unitless)} \end{symbDescription} \\ \midrule \\ - Notes & ${{T_{melt}}^{P}}$, ${t_{final}}$, ${T_{init}}$, ${h_{P}}$, ${m_{P}}$, ${{C_{P}}^{S}}$, ${{C_{P}}^{S}}$ form (\hyperref[IM:eBalanceOnWtr]{IM: eBalanceOnWtr}). The input is constrained so that ${T_{init}}<{{T_{melt}}^{P}}$ (\hyperref[assumpPIS]{A: PCM-Initially-Solid}) ${T_{P}}$, $0