This section collects and defines all the data needed to build the instance models.
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
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 Source – RefBy FR:Find-Mass
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
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
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
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
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
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
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 IM:eBalanceOnPCM and TM:latentHtE
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