Symbols
$c_p$	Specific heat, (J/kg K)
$g$	Gravitational acceleration, (m s−2)
$k$	Thermal conductivity, (W/m K)
$P$	Pressure, (Pa)
$T$	Temperature, (K)
$T_m$	Melting Point, (K)
$T_l$	Liquid temperature, (K)
$T_s$	Solid temperature, (K)
$T_{in}$	Initial temperature, (K)
$\mathsf{\Delta }T$	Transition temperature range, (K)
$t$	Time, (s)
$\overrightarrow{V}$	Velocity Vector, (m s−1)
$u$	Velocity in x-direction, (m s −1)
$v$	Velocity in y-direction, (m s−1)
$h$	Sensible enthalpy, (kJ/kg)
$H$	Total enthalpy, (kJ/kg)
$\mathsf{\Delta }H$	Latent heat, (kJ/kg)
$h_{ref}$	Enthalpy reference, (kJ/kg)
D	Smoothed Delta Dirac function
$S_a$	Source term of porosity function, (kg.s2.m−2)
$S_b$	Boussinesq approximation of buoyancy force, (kg.s2.m−2)
C	Mushy region morphology constant, (kg/ m3.s)
dp	Nanoparticle diameter, (m)
Kb	Boltzmann constant
Greek letters
$\beta$	Thermal expansion coefficient, (K−1)
$\mu$	Dynamic viscosity, (Pa.s)
$\kappa$	Permeability, (m2)
$\epsilon$	Porosity (liquid fraction)
$\eta$	Porosity function
$\rho$	Density (kg/m3)
$\varphi$	Nanoparticle concentration
Subscript
s	Solid state
l	Liquid state
n	Nanoparticle
Abbreviations
PCM	Phase Change Material
HTF	Heat Transfer Fluid
NEPCM	Nanoparticle Enhanced Phase Change Material
TES	Thermal Energy Storage