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Data Definitions

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

Mass of water

Refname	DD:waterMass
Label	Mass of water
Symbol	${m_{\text{W}}}$
Units	${\text{kg}}$
Equation	${m_{\text{W}}}={V_{\text{W}}}\,{ρ_{\text{W}}}$
Description	${m_{\text{W}}}$ is the mass of water ( ${\text{kg}}$ ) ${V_{\text{W}}}$ is the volume of water ( ${\text{m}^{3}}$ ) ${ρ_{\text{W}}}$ is the density of water ( $\frac{\text{kg}}{\text{m}^{3}}$ )
Source	–
RefBy	FR:Find-Mass

Volume of water

Refname	DD:waterVolume.pcm
Label	Volume of water
Symbol	${V_{\text{W}}}$
Units	${\text{m}^{3}}$
Equation	${V_{\text{W}}}={V_{\text{tank}}}-{V_{\text{P}}}$
Description	${V_{\text{W}}}$ is the volume of water ( ${\text{m}^{3}}$ ) ${V_{\text{tank}}}$ is the volume of the cylindrical tank ( ${\text{m}^{3}}$ ) ${V_{\text{P}}}$ is the volume of PCM ( ${\text{m}^{3}}$ )
Notes	Based on A:Volume-Coil-Negligible. ${V_{\text{tank}}}$ is defined in DD:tankVolume.
Source	–
RefBy	FR:Find-Mass

Volume of the cylindrical tank

Refname	DD:tankVolume
Label	Volume of the cylindrical tank
Symbol	${V_{\text{tank}}}$
Units	${\text{m}^{3}}$
Equation	${V_{\text{tank}}}=π\,\left(\frac{D}{2}\right)^{2}\,L$
Description	${V_{\text{tank}}}$ is the volume of the cylindrical tank ( ${\text{m}^{3}}$ ) $π$ is the ratio of circumference to diameter for any circle (Unitless) $D$ is the diameter of tank ( ${\text{m}}$ ) $L$ is the length of tank ( ${\text{m}}$ )
Source	–
RefBy	DD:waterVolume_pcm and FR:Find-Mass

ODE parameter for water related to decay time

Refname	DD:balanceDecayRate
Label	ODE parameter for water related to decay time
Symbol	${τ_{\text{W}}}$
Units	${\text{s}}$
Equation	${τ_{\text{W}}}=\frac{{m_{\text{W}}}\,{C_{\text{W}}}}{{h_{\text{C}}}\,{A_{\text{C}}}}$
Description	${τ_{\text{W}}}$ is the ODE parameter for water related to decay time ( ${\text{s}}$ ) ${m_{\text{W}}}$ is the mass of water ( ${\text{kg}}$ ) ${C_{\text{W}}}$ is the specific heat capacity of water ( $\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}$ ) ${h_{\text{C}}}$ is the convective heat transfer coefficient between coil and water ( $\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}$ ) ${A_{\text{C}}}$ is the heating coil surface area ( ${\text{m}^{2}}$ )
Source	koothoor2013
RefBy	IM:eBalanceOnWtr and FR:Output-Input-Derived-Values

ODE parameter related to decay rate

Refname	DD:balanceDecayTime
Label	ODE parameter related to decay rate
Symbol	$η$
Units	Unitless
Equation	$η=\frac{{h_{\text{P}}}\,{A_{\text{P}}}}{{h_{\text{C}}}\,{A_{\text{C}}}}$
Description	$η$ is the ODE parameter related to decay rate (Unitless) ${h_{\text{P}}}$ is the convective heat transfer coefficient between PCM and water ( $\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}$ ) ${A_{\text{P}}}$ is the phase change material surface area ( ${\text{m}^{2}}$ ) ${h_{\text{C}}}$ is the convective heat transfer coefficient between coil and water ( $\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}$ ) ${A_{\text{C}}}$ is the heating coil surface area ( ${\text{m}^{2}}$ )
Source	koothoor2013
RefBy	IM:eBalanceOnWtr and FR:Output-Input-Derived-Values

ODE parameter for solid PCM

Refname	DD:balanceSolidPCM
Label	ODE parameter for solid PCM
Symbol	${{τ_{\text{P}}}^{\text{S}}}$
Units	${\text{s}}$
Equation	${{τ_{\text{P}}}^{\text{S}}}=\frac{{m_{\text{P}}}\,{{C_{\text{P}}}^{\text{S}}}}{{h_{\text{P}}}\,{A_{\text{P}}}}$
Description	${{τ_{\text{P}}}^{\text{S}}}$ is the ODE parameter for solid PCM ( ${\text{s}}$ ) ${m_{\text{P}}}$ is the mass of phase change material ( ${\text{kg}}$ ) ${{C_{\text{P}}}^{\text{S}}}$ is the specific heat capacity of PCM as a solid ( $\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}$ ) ${h_{\text{P}}}$ is the convective heat transfer coefficient between PCM and water ( $\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}$ ) ${A_{\text{P}}}$ is the phase change material surface area ( ${\text{m}^{2}}$ )
Source	lightstone2012
RefBy	IM:eBalanceOnPCM and FR:Output-Input-Derived-Values

ODE parameter for liquid PCM

Refname	DD:balanceLiquidPCM
Label	ODE parameter for liquid PCM
Symbol	${{τ_{\text{P}}}^{\text{L}}}$
Units	${\text{s}}$
Equation	${{τ_{\text{P}}}^{\text{L}}}=\frac{{m_{\text{P}}}\,{{C_{\text{P}}}^{\text{L}}}}{{h_{\text{P}}}\,{A_{\text{P}}}}$
Description	${{τ_{\text{P}}}^{\text{L}}}$ is the ODE parameter for liquid PCM ( ${\text{s}}$ ) ${m_{\text{P}}}$ is the mass of phase change material ( ${\text{kg}}$ ) ${{C_{\text{P}}}^{\text{L}}}$ is the specific heat capacity of PCM as a liquid ( $\frac{\text{J}}{\text{kg}{}^{\circ}\text{C}}$ ) ${h_{\text{P}}}$ is the convective heat transfer coefficient between PCM and water ( $\frac{\text{W}}{\text{m}^{2}{}^{\circ}\text{C}}$ ) ${A_{\text{P}}}$ is the phase change material surface area ( ${\text{m}^{2}}$ )
Source	lightstone2012
RefBy	IM:eBalanceOnPCM and FR:Output-Input-Derived-Values

Specific latent heat of fusion

Refname	DD:htFusion
Label	Specific latent heat of fusion
Symbol	${H_{\text{f}}}$
Units	$\frac{\text{J}}{\text{kg}}$
Equation	${H_{\text{f}}}=\frac{Q}{m}$
Description	${H_{\text{f}}}$ is the specific latent heat of fusion ( $\frac{\text{J}}{\text{kg}}$ ) $Q$ is the latent heat ( ${\text{J}}$ ) $m$ is the mass ( ${\text{kg}}$ )
Notes	The specific latent heat of fusion (also known as the enthalpy of fusion) of a substance is the heat energy required ( $Q$ ) to change the state of a unit of the mass ( $m$ ) of the substance from solid to liquid, at constant pressure.
Source	bueche1986 (pg. 282)
RefBy	IM:heatEInPCM and DD:meltFrac

Melt fraction

Refname	DD:meltFrac
Label	Melt fraction
Symbol	$ϕ$
Units	Unitless
Equation	$ϕ=\frac{{Q_{\text{P}}}}{{H_{\text{f}}}\,{m_{\text{P}}}}$
Description	$ϕ$ is the melt fraction (Unitless) ${Q_{\text{P}}}$ is the latent heat energy added to PCM ( ${\text{J}}$ ) ${H_{\text{f}}}$ is the specific latent heat of fusion ( $\frac{\text{J}}{\text{kg}}$ ) ${m_{\text{P}}}$ is the mass of phase change material ( ${\text{kg}}$ )
Notes	The value of $ϕ$ is constrained to $0\leq{}ϕ\leq{}1$ . DD:htFusion
Source	koothoor2013
RefBy	TM:latentHtE and IM:eBalanceOnPCM

Aspect ratio

Refname	DD:aspectRatio
Label	Aspect ratio
Symbol	$\mathit{AR}$
Units	Unitless
Equation	$\mathit{AR}=\frac{D}{L}$
Description	$\mathit{AR}$ is the aspect ratio (Unitless) $D$ is the diameter of tank ( ${\text{m}}$ ) $L$ is the length of tank ( ${\text{m}}$ )
Source	–
RefBy