Buoyancy induced convection in a porous cavity with sinusoidally and partially thermally active sidewalls under local thermal non-equilibrium condition

Steady non-Darcy natural convection in a porous cavity with non-uniform thermal boundary condition is studied numerically by adopting the local thermal non-equilibrium (LTNE) model in this paper. The top and bottom walls of the cavity are adiabatic. The left vertical wall is partially heated and cooled by sinusoidal temperature profile and the right side wall of the cavity is partially cooled by uniform thermal boundary condition. The results show that, the oscillation amplitude of the local Nusselt number profiles (Nufy, Nusy) along the Y coordinate decreases with the increase of H. The difference of the local Nusselt numbers between different cases of partial cooling (case A-case D) can be reduced by increasing of N. The difference of solid-to-fluid temperature differences between different cases of partial cooling can be reduced by increasing of H and γ. Positive values of the average Nusselt number appear at the left side wall of the porous cavity, which indicates that there exists heat transfer along the positive direction of the X axis in the porous cavity. Compared with the left wall of the cavity, it is faster for the right wall to reach the thermal equilibrium state, which approaches a constant value for low values of H (H = 3000).