Natural convection in a porous rectangular enclosure with sinusoidal temperature distributions on both side walls using a thermal non-equilibrium model

This study reports a numerical investigation of the natural convective flow and heat transfer in a rectangular cavity filled with a heat-generating porous medium by adopting the local thermal non-equilibrium model. The top and bottom walls of the enclosure are adiabatic and the left and right walls are partially heated and partially cooled by sinusoidal temperature profile. The results show that periodic variations with positive and negative values appear in the isotherms for fluid phase and solid phase, and the periodicity increases with the increase of N. The phase deviation has significant influence on fluid flow and heat transfer in the porous cavity. When N is large enough (N = 32), patterns of streamlines, isotherms for fluid phase and solid phase display like that of uniform thermal boundary condition case, and the total heat transfer rate through the whole cavity is close to that resulted by uniform thermal boundary condition. The heat transfer of porous cavity can be enhanced by sinusoidal thermal boundary condition and the phase deviation has tiny effect on the heat transfer of cavity when N is large enough (N = 32). The increase of inter-phase heat transfer coefficient leads to faster reduction of Q with the increase of periodicity parameter.