Analysis of mixed convection in a vertical porous layer using non-equilibrium model

The problem of two-dimensional steady mixed convection in a vertical porous layer is investigated numerically in the present paper using the thermally non-equilibrium model. The vertical porous layer is assumed to have a finite isothermally heated segment on one vertical wall which is otherwise adiabatic and the other vertical wall is cooled to a constant temperature. Non-dimensionalization of the governing equations results in four parameters for both aiding and opposing flows: (1) Ra, Rayleigh number (2) Pe, Péclet number (3) K_r, thermal conductivity ratio parameter, and (4) H, heat transfer coefficient parameter. The numerical results are presented for 0.01  H  100, 0.01  K_r  100, 0.01  Pe  100 and Ra = 10, 50 and 100. The results show that, the thermal equilibrium model cannot predict the average Nusselt number correctly for small values of H × K_r. In both the aiding and opposing flows, the total average Nusselt number is decreasing with increasing the heat transfer coefficient parameter at low values of Pe, while for high values of Pe, higher H will enhance the total heat transfer rate. Increasing the thermal conductivity ratio leads to increase in the total average Nusselt number. It is found also that the total average Nusselt number depends strongly on the thermal conductivity ratio parameter and depends slightly on the heat transfer coefficient parameter.