Thermal Performance of the Melting of the Phase-change Material n-octadecane in a Trapezoidal Cavitys

This study models the thermal performance during the melting of the phase-change material (PCM) n-octadecane in a trapezoidal cavity. The left inclined wall is subjected to a variable heat flux, whilst the other three walls are kept adiabatic. The governing heat- and mass-transfer equations are based on the Navier–Stokes and energy equations, formulated in terms of stream-vorticity variables. Phase change is accounted for using the enthalpy-porosity method, and latent heat is represented using an apparent heat capacity. These equations are discretised using the finite difference method according to an explicit scheme with an adaptive time step. The resulting systems of algebraic equations are solved using the Gauss–Seidel algorithm. The computational software used is MATLAB. The numerical results obtained are presented in the form of liquid fraction fields, isotherms, velocity fields and the melting front within the cavity. The results show that melting occurs in two successive phases: a phase dominated by conduction in the initial state, followed by a phase dominated by natural convection. Indeed, between 7 and 18 hours, the molten PCM content is 73.04%, offering solid foundations for the thermal optimization of buildings in hot climates.