Software Requirements Specification for Solar Water Heating Systems

Thulasi Jegatheesan

Table of Contents

An outline of all sections included in this SRS is recorded here for easy reference.

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 of Units lists the symbol, a description, and the SI name.

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

Table of Units

Table of Symbols

The symbols used in this document are summarized in the Table of Symbols 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 with no phase change material. The symbols are listed in alphabetical order. For vector quantities, the units shown are for each component of the vector.

Symbol Description Units
AC Heating coil surface area m2
ACmax Maximum surface area of coil m2
Ain Surface area over which heat is transferred in m2
Aout Surface area over which heat is transferred out m2
Atol Absolute tolerance --
ARmax Maximum aspect ratio --
ARmin Minimum aspect ratio --
C Specific heat capacity \(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\)
CL Specific heat capacity of a liquid \(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\)
CW Specific heat capacity of water \(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\)
CWmax Maximum specific heat capacity of water \(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\)
CWmin Minimum specific heat capacity of water \(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\)
D Diameter of tank m
E Sensible heat J
EW Change in heat energy in the water J
g Volumetric heat generation per unit volume \(\frac{\text{W}}{\text{m}^{3}}\)
h Convective heat transfer coefficient \(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\)
hC Convective heat transfer coefficient between coil and water \(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\)
hCmax Maximum convective heat transfer coefficient between coil and water \(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\)
hCmin Minimum convective heat transfer coefficient between coil and water \(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\)
L Length of tank m
Lmax Maximum length of tank m
Lmin Minimum length of tank m
m Mass kg
mW Mass of water kg
n̂ Normal vector --
q Heat flux \(\frac{\text{W}}{\text{m}^{2}}\)
qC Heat flux into the water from the coil \(\frac{\text{W}}{\text{m}^{2}}\)
qin Heat flux input \(\frac{\text{W}}{\text{m}^{2}}\)
qout Heat flux output \(\frac{\text{W}}{\text{m}^{2}}\)
q Thermal flux vector \(\frac{\text{W}}{\text{m}^{2}}\)
Rtol Relative tolerance --
S Surface m2
T Temperature °C
ΔT Change in temperature °C
TC Temperature of the heating coil °C
Tenv Temperature of the environment °C
Tinit Initial temperature °C
TW Temperature of the water °C
t Time s
tfinal Final time s
tfinalmax Maximum final time s
tstep Time step for simulation s
V Volume m3
Vtank Volume of the cylindrical tank m3
VW Volume of water m3
π Ratio of circumference to diameter for any circle --
ρ Density \(\frac{\text{kg}}{\text{m}^{3}}\)
ρW Density of water \(\frac{\text{kg}}{\text{m}^{3}}\)
ρWmax Maximum density of water \(\frac{\text{kg}}{\text{m}^{3}}\)
ρWmin Minimum density of water \(\frac{\text{kg}}{\text{m}^{3}}\)
τW ODE parameter for water related to decay time s
∇ Gradient --

Table of Symbols

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
PS Physical System Description
R Requirement
RefBy Referenced by
Refname Reference Name
SRS Software Requirements Specification
SWHSNoPCM Solar Water Heating System With No Phase Change Material
TM Theoretical Model
UC Unlikely Change
Uncert. Typical Uncertainty

Abbreviations and Acronyms

Introduction

Due to increasing costs, diminishing availability, and negative environmental impact of fossil fuels, the demand is high for renewable energy sources and energy storage technology. Solar Water Heating System with no Phase Change Material provide a novel way of storing energy.

The following section provides an overview of the Software Requirements Specification (SRS) for solar water heating systems with no phase change material The developed program will be referred to as Solar Water Heating System With No Phase Change Material (SWHSNoPCM) based on the original, manually created version of SWHSNoPCM. This section explains the purpose of this document, the scope of the requirements, the characteristics of the intended reader, and the organization of the document.

Purpose of Document

The primary purpose of this document is to record the requirements of SWHSNoPCM. Goals, assumptions, theoretical models, definitions, and other model derivation information are specified, allowing the reader to fully understand and verify the purpose and scientific basis of SWHSNoPCM. With the exception of system constraints, this SRS will remain abstract, describing what problem is being solved, but not 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.

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 SWHSNoPCM can have a lower level of expertise, as explained in Sec:User Characteristics.

Organization of Document

The organization of this document follows the template for an SRS for scientific computing software proposed by koothoor2013, smithLai2005, smithEtAl2007, and smithKoothoor2016. 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 and trace back to find any additional information they require.

The goal statements are refined to the theoretical models and the theoretical models to the instance models. The instance model to be solved is referred to as IM:eBalanceOnWtr. The instance model provides the Ordinary Differential Equation (ODE) that models the solar water heating system with no phase change material. SWHSNoPCM solves this ODE.

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 (SWHSNoPCM). Arrows are used to show the data flow between the system and its environment.

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

SWHSNoPCM 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
  • SWHSNoPCM 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 SWHSNoPCM 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

A system is needed to investigate the heating of water in 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.
  • 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 SWHSNoPCM, 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.)

Solar water heating tank, with heat flux from heating coil of <em>q<sub>C</sub></em>
Figure: Solar water heating tank, with heat flux from heating coil of qC

Goal Statements

Given the temperature of the heating coil, the initial temperature of the water, and the material properties, the goal statements are:

Predict-Water-Temperature: Predict the temperature of the water over time.

Predict-Water-Energy: Predict the change in heat energy in the water over time.

Solution Characteristics Specification

The instance models that govern SWHSNoPCM are presented in the Instance Model Section. 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 models by filling in the missing information for the physical system. The assumptions refine the scope by providing more detail.

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. (RefBy: TM:consThermE.)

Heat-Transfer-Coeffs-Constant: All heat transfer coefficients are constant over time. (RefBy: TM: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. (RefBy: GD:rocTempSimp.)

Density-Water-Constant-over-Volume: The density of water has no spatial variation; that is, it is constant over their entire volume. (RefBy: GD:rocTempSimp.)

Specific-Heat-Energy-Constant-over-Volume: The specific heat capacity of water has no spatial variation; that is, it is constant over its entire volume. (RefBy: GD:rocTempSimp.)

Newton-Law-Convective-Cooling-Coil-Water: Newton's law of convective cooling applies between the heating coil and the water. (RefBy: GD:htFluxWaterFromCoil.)

Temp-Heating-Coil-Constant-over-Time: The temperature of the heating coil is constant over time. (RefBy: GD:htFluxWaterFromCoil and LC:Temperature-Coil-Variable-Over-Day.)

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

Charging-Tank-No-Temp-Discharge: The model only accounts for charging the tank, not discharging. The temperature of the water can only increase, or remain constant; it cannot decrease. This implies that the initial temperature is less than (or equal to) the temperature of the heating coil. (RefBy: LC:Discharging-Tank.)

Water-Always-Liquid: The operating temperature range of the system is such that the material (water in this case) 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. (RefBy: TM:sensHtE, IM:eBalanceOnWtr, UC:Water-Fixed-States, and IM:heatEInWtr.)

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

No-Internal-Heat-Generation-By-Water: No internal heat is generated by the water; therefore, the volumetric heat generation per unit volume is zero. (RefBy: IM:eBalanceOnWtr and UC:No-Internal-Heat-Generation.)

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

Volume-Coil-Negligible: When considering the volume of water in the tank, the volume of the heating coil is assumed to be negligible. (RefBy: DD:waterVolume_nopcm.)

Theoretical Models

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

Refname TM:consThermE
Label

Conservation of thermal energy
Equation \[-∇\cdot{}\symbf{q}+g=ρ\,C\,\frac{\,\partial{}T}{\,\partial{}t}\]
Description
  • ∇ is the gradient (Unitless)
  • q is the thermal flux vector (\(\frac{\text{W}}{\text{m}^{2}}\))
  • g is the volumetric heat generation per unit volume (\(\frac{\text{W}}{\text{m}^{3}}\))
  • ρ is the density (\(\frac{\text{kg}}{\text{m}^{3}}\))
  • C is the specific heat capacity (\(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\))
  • 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 given material.

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
Refname TM:sensHtE
Label

Sensible heat energy (no state change)
Equation \[E={C^{\text{L}}}\,m\,ΔT\]
Description
  • E is the sensible heat (J)
  • CL is the specific heat capacity of a liquid (\(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\))
  • m is the mass (kg)
  • ΔT is the change in temperature (°C)
Notes

E occurs as long as the material does not reach a temperature where a phase change occurs, as assumed in A:Water-Always-Liquid.

Source

Definition of Sensible Heat

RefBy

IM:heatEInWtr
Refname TM:nwtnCooling
Label

Newton's law of cooling
Equation \[q\left(t\right)=h\,ΔT\left(t\right)\]
Description
  • q is the heat flux (\(\frac{\text{W}}{\text{m}^{2}}\))
  • t is the time (s)
  • h is the convective heat transfer coefficient (\(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\))
  • 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.

h is assumed to be independent of T (from A:Heat-Transfer-Coeffs-Constant).

ΔT(t) = T(t)−Tenv(t) is the time-dependant thermal gradient between the environment and the object.

Source

incroperaEtAl2007 (pg. 8)

RefBy

GD:htFluxWaterFromCoil

General Definitions

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

Refname GD:rocTempSimp
Label

Simplified rate of change of temperature
Equation \[m\,C\,\frac{\,dT}{\,dt}={q_{\text{in}}}\,{A_{\text{in}}}-{q_{\text{out}}}\,{A_{\text{out}}}+g\,V\]
Description
  • m is the mass (kg)
  • C is the specific heat capacity (\(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\))
  • t is the time (s)
  • T is the temperature (°C)
  • qin is the heat flux input (\(\frac{\text{W}}{\text{m}^{2}}\))
  • Ain is the surface area over which heat is transferred in (m2)
  • qout is the heat flux output (\(\frac{\text{W}}{\text{m}^{2}}\))
  • Aout is the surface area over which heat is transferred out (m2)
  • g is the volumetric heat generation per unit volume (\(\frac{\text{W}}{\text{m}^{3}}\))
  • V is the volume (m3)
Source

--
RefBy

GD:rocTempSimp and IM:eBalanceOnWtr

Detailed derivation of simplified rate of change of temperature:

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

\[-\int_{V}{∇\cdot{}\symbf{q}}\,dV+\int_{V}{g}\,dV=\int_{V}{ρ\,C\,\frac{\,\partial{}T}{\,\partial{}t}}\,dV\]

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:

\[-\int_{S}{\symbf{q}\cdot{}\symbf{\hat{n}}}\,dS+\int_{V}{g}\,dV=\int_{V}{ρ\,C\,\frac{\,\partial{}T}{\,\partial{}t}}\,dV\]

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

\[{q_{\text{in}}}\,{A_{\text{in}}}-{q_{\text{out}}}\,{A_{\text{out}}}+g\,V=\int_{V}{ρ\,C\,\frac{\,\partial{}T}{\,\partial{}t}}\,dV\]

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:Density-Water-Constant-over-Volume, and A:Specific-Heat-Energy-Constant-over-Volume, we have:

\[ρ\,C\,V\,\frac{\,dT}{\,dt}={q_{\text{in}}}\,{A_{\text{in}}}-{q_{\text{out}}}\,{A_{\text{out}}}+g\,V\]

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

\[m\,C\,\frac{\,dT}{\,dt}={q_{\text{in}}}\,{A_{\text{in}}}-{q_{\text{out}}}\,{A_{\text{out}}}+g\,V\]
Refname GD:htFluxWaterFromCoil
Label

Heat flux into the water from the coil
Units

\(\frac{\text{W}}{\text{m}^{2}}\)
Equation \[{q_{\text{C}}}={h_{\text{C}}}\,\left({T_{\text{C}}}-{T_{\text{W}}}\left(t\right)\right)\]
Description
  • qC is the heat flux into the water from the coil (\(\frac{\text{W}}{\text{m}^{2}}\))
  • hC is the convective heat transfer coefficient between coil and water (\(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\))
  • TC is the temperature of the heating coil (°C)
  • TW is the temperature of the water (°C)
  • t is the time (s)
Notes

qC is found by assuming that Newton's law of cooling applies (A:Newton-Law-Convective-Cooling-Coil-Water). This law (defined in TM:nwtnCooling) is used on the surface of the heating coil.

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

Source

koothoor2013
RefBy

IM:eBalanceOnWtr

Data Definitions

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

Refname DD:waterMass
Label

Mass of water
Symbol

mW
Units

kg
Equation \[{m_{\text{W}}}={V_{\text{W}}}\,{ρ_{\text{W}}}\]
Description
  • mW is the mass of water (kg)
  • VW is the volume of water (m3)
  • ρW is the density of water (\(\frac{\text{kg}}{\text{m}^{3}}\))
Source

--
RefBy

FR:Find-Mass
Refname DD:waterVolume.nopcm
Label

Volume of water
Symbol

VW
Units

m3
Equation \[{V_{\text{W}}}={V_{\text{tank}}}\]
Description
  • VW is the volume of water (m3)
  • Vtank is the volume of the cylindrical tank (m3)
Notes

Based on A:Volume-Coil-Negligible. Vtank is defined in DD:tankVolume.

Source

--
RefBy

FR:Find-Mass
Refname DD:tankVolume
Label

Volume of the cylindrical tank
Symbol

Vtank
Units

m3
Equation \[{V_{\text{tank}}}=π\,\left(\frac{D}{2}\right)^{2}\,L\]
Description
  • Vtank is the volume of the cylindrical tank (m3)
  • π is the ratio of circumference to diameter for any circle (Unitless)
  • D is the diameter of tank (m)
  • L is the length of tank (m)
Source

--
RefBy

DD:waterVolume_nopcm and FR:Find-Mass

Refname DD:balanceDecayRate
Label

ODE parameter for water related to decay time

Symbol

τW
Units

s
Equation \[{τ_{\text{W}}}=\frac{{m_{\text{W}}}\,{C_{\text{W}}}}{{h_{\text{C}}}\,{A_{\text{C}}}}\]
Description
  • τW is the ODE parameter for water related to decay time (s)
  • mW is the mass of water (kg)
  • CW is the specific heat capacity of water (\(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\))
  • hC is the convective heat transfer coefficient between coil and water (\(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\))
  • AC is the heating coil surface area (m2)
Source

koothoor2013
RefBy

IM:eBalanceOnWtr and FR:Output-Input-Derived-Values

Instance Models

This section transforms the problem defined in the problem description into one which is expressed in mathematical terms. It uses concrete symbols defined in the data definitions to replace the abstract symbols in the models identified in theoretical models and general definitions.

The goal GS:Predict-Water-Temperature is met by IM:eBalanceOnWtr and the goal GS:Predict-Water-Energy is met by IM:heatEInWtr.

Refname IM:eBalanceOnWtr
Label

Energy balance on water to find the temperature of the water

Input

TC, Tinit, tfinal, AC, hC, CW, mW

Output

TW
Input Constraints \[{T_{\text{C}}}\geq{}{T_{\text{init}}}\]
Output Constraints
Equation \[\frac{\,d{T_{\text{W}}}}{\,dt}+\frac{1}{{τ_{\text{W}}}}\,{{T_{\text{W}}}}=\frac{1}{{τ_{\text{W}}}}\,{T_{\text{C}}}\]
Description
  • t is the time (s)
  • TW is the temperature of the water (°C)
  • τW is the ODE parameter for water related to decay time (s)
  • TC is the temperature of the heating coil (°C)
Notes

τW is calculated from DD:balanceDecayRate.

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).

Source

koothoor2013 (with PCM removed)

RefBy

UC:No-Internal-Heat-Generation, FR:Output-Values, FR:Find-Mass, and FR:Calculate-Values

Detailed 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 in the tank VW, which has mass mW and specific heat capacity, CW. Heat transfer occurs in the water from the heating coil as qC (GD:htFluxWaterFromCoil), over area AC. No heat transfer occurs to the outside of the tank, since it has been assumed to be perfectly insulated (A:Perfect-Insulation-Tank). Since the assumption is made that no internal heat is generated (A:No-Internal-Heat-Generation-By-Water), g = 0. Therefore, the equation for GD:rocTempSimp can be written as:

\[{m_{\text{W}}}\,{C_{\text{W}}}\,\frac{\,d{T_{\text{W}}}}{\,dt}={q_{\text{C}}}\,{A_{\text{C}}}\]

Using GD:htFluxWaterFromCoil for qC, this can be written as:

\[{m_{\text{W}}}\,{C_{\text{W}}}\,\frac{\,d{T_{\text{W}}}}{\,dt}={h_{\text{C}}}\,{A_{\text{C}}}\,\left({T_{\text{C}}}-{T_{\text{W}}}\right)\]

Dividing Equation (2) by mW CW, we obtain:

\[\frac{\,d{T_{\text{W}}}}{\,dt}=\frac{{h_{\text{C}}}\,{A_{\text{C}}}}{{m_{\text{W}}}\,{C_{\text{W}}}}\,\left({T_{\text{C}}}-{T_{\text{W}}}\right)\]

By substituting τW (from DD:balanceDecayRate), this can be written as:

\[\frac{\,d{T_{\text{W}}}}{\,dt}=\frac{1}{{τ_{\text{W}}}}\,\left({T_{\text{C}}}-{T_{\text{W}}}\right)\]
Refname IM:heatEInWtr
Label

Heat energy in the water
Input

Tinit, mW, CW, mW

Output

EW
Input Constraints
Output Constraints
Equation \[{E_{\text{W}}}\left(t\right)={C_{\text{W}}}\,{m_{\text{W}}}\,\left({T_{\text{W}}}\left(t\right)-{T_{\text{init}}}\right)\]
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 (\(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\))
  • 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.

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:Output-Values and FR:Calculate-Values

Data Constraints

The Data Constraints Table shows the data constraints on the input variables. 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.

Var Physical Constraints Software Constraints Typical Value Uncert.
AC AC > 0 AC ≤ ACmax 0.12 m2 10%
CW CW > 0 CWmin < CW < CWmax 4186 \(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\) 10%
D D > 0 ARmin ≤ D ≤ ARmax 0.412 m 10%
hC hC > 0 hCmin ≤ hC ≤ hCmax 1000 \(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\) 10%
L L > 0 Lmin ≤ L ≤ Lmax 1.5 m 10%
TC 0 < TC < 100 -- 50 °C 10%
Tinit 0 < Tinit < 100 -- 40 °C 10%
tfinal tfinal > 0 tfinal < tfinalmax 50000 s 10%
tstep 0 < tstep < tfinal -- 0.01 s 10%
ρW ρW > 0 ρWmin < ρW ≤ ρWmax 1000 \(\frac{\text{kg}}{\text{m}^{3}}\) 10%

Input Data Constraints

Properties of a Correct Solution

The Data Constraints Table shows the data constraints on the output variables. The column for physical constraints gives the physical limitations on the range of values that can be taken by the variable.

Var Physical Constraints
TW Tinit ≤ TW ≤ TC
EW EW ≥ 0

Output Data Constraints

Requirements

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

Functional Requirements

This section provides the functional requirements, the tasks and behaviours that the software is expected to complete.

Input-Initial-Values: Input the following values described in the table for Required Inputs, which define the tank parameters, material properties, and initial conditions.

Find-Mass: Use the inputs in FR:Input-Initial-Values to find the mass needed for IM:eBalanceOnWtr, using DD:waterMass, DD:waterVolume_nopcm, and DD:tankVolume.

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

Output-Input-Derived-Values: Output the input values and derived values in the following list: the values (from FR:Input-Initial-Values), the mass (from FR:Find-Mass), and τW (from DD:balanceDecayRate).

Calculate-Values: Calculate the following values: TW(t) (from IM:eBalanceOnWtr) and EW(t) (from IM:heatEInWtr).

Output-Values: Output TW(t) (from IM:eBalanceOnWtr) and EW(t) (from IM:heatEInWtr).

Symbol Description Units
AC Heating coil surface area m2
Atol Absolute tolerance --
CW Specific heat capacity of water \(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\)
D Diameter of tank m
hC Convective heat transfer coefficient between coil and water \(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\)
L Length of tank m
Rtol Relative tolerance --
TC Temperature of the heating coil °C
Tinit Initial temperature °C
tfinal Final time s
tstep Time step for simulation s
ρW Density of water \(\frac{\text{kg}}{\text{m}^{3}}\)

Required Inputs following FR:Input-Initial-Values

Non-Functional Requirements

This section provides the non-functional requirements, the qualities that the software is expected to exhibit.

Correctness: The outputs of the code have the properties of a correct solution.

Verifiability: The code is tested with complete verification and validation plan.

Understandability: The code is modularized with complete module guide and module interface specification.

Reusability: The code is modularized.

Maintainability: If a likely change is made to the finished software, it will take at most 10% of the original development time, assuming the same development resources are available.

Likely Changes

This section lists the likely changes to be made to the software.

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. That is, increasing the temperature of the water to match the temperature of the coil. A more complete model would also account for discharging of the tank.

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

Unlikely Changes

This section lists the unlikely changes to be made to the software.

Water-Fixed-States: A:Water-Always-Liquid - It is unlikely for the change of water from liquid to a solid, or from liquid to gas to be considered.

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

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 column of that component that are marked with an "X" should be modified as well. Tab:TraceMatAvsA shows the dependencies of the assumptions on each other. Tab:TraceMatAvsAll shows the dependencies of the data definitions, theoretical models, general definitions, instance models, requirements, likely changes, and unlikely changes on the assumptions. Tab:TraceMatRefvsRef shows the dependencies of the data definitions, theoretical models, general definitions, and instance models on each other. Tab:TraceMatAllvsR shows the dependencies of the requirements and goal statements on the data definitions, theoretical models, general definitions, and instance models.

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:TraceGraphAvsA shows the dependencies of assumptions on each other. Fig:TraceGraphAvsAll shows the dependencies of data definitions, theoretical models, general definitions, instance models, requirements, likely changes, and unlikely changes on the assumptions. Fig:TraceGraphRefvsRef shows the dependencies of data definitions, theoretical models, general definitions, and instance models on each other. Fig:TraceGraphAllvsR shows the dependencies of requirements and goal statements on the data definitions, theoretical models, general definitions, and instance models. Fig:TraceGraphAllvsAll shows the dependencies of dependencies of assumptions, models, definitions, requirements, goals, and changes with each other.

TraceGraphAvsA
Figure: TraceGraphAvsA
TraceGraphAvsAll
Figure: TraceGraphAvsAll
TraceGraphRefvsRef
Figure: TraceGraphRefvsRef
TraceGraphAllvsR
Figure: TraceGraphAllvsR
TraceGraphAllvsAll
Figure: TraceGraphAllvsAll

For convenience, the following graphs can be found at the links below:

Values of Auxiliary Constants

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

Symbol Description Value Unit
ACmax maximum surface area of coil 100000 m2
ARmax maximum aspect ratio 100 --
ARmin minimum aspect ratio 0.01 --
CWmax maximum specific heat capacity of water 4210 \(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\)
CWmin minimum specific heat capacity of water 4170 \(\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}\)
hCmax maximum convective heat transfer coefficient between coil and water 10000 \(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\)
hCmin minimum convective heat transfer coefficient between coil and water 10 \(\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}\)
Lmax maximum length of tank 50 m
Lmin minimum length of tank 0.1 m
tfinalmax maximum final time 86400 s
ρWmax maximum density of water 1000 \(\frac{\text{kg}}{\text{m}^{3}}\)
ρWmin minimum density of water 950 \(\frac{\text{kg}}{\text{m}^{3}}\)

Auxiliary Constants

References