## 6 Conclusions
\begin{tabular}{l l} \(Re_{d}\) & Pore Reynolds number, \(Re_{d}=Red_{p}/\varepsilon H\) \\ \(Rc\) & Heat capacity ratio, \(Rc=(\rho c_{p})_{s}/(\rho c_{p})_{f}\) \\ \(S_{i}\) & Source terms \\ \(S_{f}(S_{g})\) & Diagonal relaxation matrix \\ \(Ste\) & Stefan number, \(Ste=C_{pf}(T_{h}-T_{m})/L_{a}\) \\ \(T\) & Temperature (\(K\)) \\ \(T_{m}\) & PCM melting temperature (\(K\)) \\ \(\Theta\) & Dimensionless temperature \\ \(t\) & Time (s) \\ \(u\), \(v\) & Velocity (\(\mathrm{m}\cdot\mathrm{s}^{-1}\)) \\ \(U_{0}\) & Inlet velocity(\(\mathrm{m}\cdot\mathrm{s}^{-1}\)) \\ \(x\), \(y\) & Cartesian coordinates (\(m\)) \\
**Greek symbols** \\ \(\
abla\) & Gradient operator \\ \(\
abla\). & Divergence operator \\ \(\alpha\) & Thermal diffusivity (\(\mathrm{m}^{2}\cdot\mathrm{s}^{-1}\)) \\ \(\beta\) & Thermal expansion coefficient (\(\mathrm{K}^{-1}\)) \\ \(\epsilon\) & Media porosity \\ \(\omega\) & Pore density (PPI) \\ \(\lambda\) & Thermal conductivity (\(\mathrm{W}\cdot\mathrm{m}^{-1}\cdot\mathrm{K}^{-1}\)) \\ \(\mu_{f}\) & Dynamic fluid viscosity (\(\mathrm{kg}\cdot\mathrm{m}^{-1}\cdot\mathrm{s}^{-1}\)) \\ \(\Gamma\) & PCM melting fraction \\ \(\
u\) & Kinematic viscosity (\(\mathrm{m}^{2}\cdot\mathrm{s}^{-1}\)) \\ \(\rho\) & Density (\(\mathrm{kg}\cdot\mathrm{m}^{-3}\)) \\ \(\tau_{a}\) & Free relaxation time \\ \(\tau_{0}/g_{f}/s\) & Single relaxation time \\ \(\tau_{i}\) & Relaxation rates \\ \(\tau_{s}\) & Viscous relaxation time \\ \(\Lambda\) & Monitor factor \\ \(\Omega\) & Collision operator \\ \(w_{i}\) & Weight coefficient in direction \(i\) \\
**Superscripts/subscripts** \\ \(e_{ff}\) & Effective \\ \(f\) & Fluid \\ \(\tilde{i}\) & Direction opposite to \(i\) \\ \(m\) & Melting \\ \(\circ\) & Initial state \\ \(Ref\) & Reference \\ \(s\) & Solid \\
**Abbreviations** \\ \(ARM\) & Adaptive mesh refinement \\ \(BGK\) & Bhatnagar-Gross-Krook \\ \(CFD\) & Computational fluid dynamics \\ \(CFL\) & Courant-Friedrichs-Lewy \\ \(CNT\) & Carbon nanotubes \\ \(DBTE\) & Discretization of Boltzmann transport equation \\ \(DSMC\) & Direct simulation Monte Carlo \\ \(DNS\) & Direct numerical simulation \\ \(DPD\) & Dissipative particle dissipation \\ \(EG\) & Expanded graphite \\ \(ES\) & Energy storage \\ \(EIU\) & European union \\ \(ESS\) & Energy storage system \\ \(FDM\) & Finite difference method \\ \(FEM\) & Finite element methods \\ \(FVM\) & Finite volume methods \\ \(GKM\) & Gas-kinetic method \\ \(\Lambda\) & \(\Lambda\) & \(\Lambda\) \\ \(\Omega\) & Collision operator \\ \(w_{i}\) & Weight coefficient in direction \(i\) \\
**Superscripts/subscripts** \\ \(e_{ff}\) & Effective \\ \(f\) & Fluid \\ \(\tilde{i}\) & Direction opposite to \(i\) \\ \(m\) & Melting \\ \(\circ\) & Initial state \\ \(Ref\) & Reference \\ \(s\) & Solid \\
**Abbreviations** \\ \(ARM\) & Adaptive mesh refinement \\ \(BGK\) & Bhatnagar-Gross-Krook \\ \(CFD\) & Computational fluid dynamics \\ \(CFL\) & Courant-Friedrichs-Lewy \\ \(CNT\) & Carbon nanotubes \\ \(DBTE\) & Discretization of Boltzmann transport equation \\ \(DSMC\) & Direct simulation Monte Carlo \\ \(DNS\) & Direct numerical simulation \\ \(DPD\) & Dissipative particle dissipation \\ \(EG\) & Expanded graphite \\ \(ES\) & Energy storage \\ \(EIU\) & European union \\ \(ESS\) & Energy storage system \\ \(FDM\) & Finite difference method \\ \(FEM\) & Finite element methods \\ \(FVM\) & Finite volume methods \\ \(GKM\) & Gas-kinetic method \\ \end{tabular}