Application of the UNIFAES discretization scheme to mixed convection in a porous layer with a cavity, using the Darcy model

Results of numerical simulations are presented on mixed concentration in a two-dimensional dimensional, horizontal, saturated porous layer, with a cav ity of varying depth on the bottom surface, heated from below. The problem formulation was based on the Darcy model to relate the velocity and the pre ssure fields, and on the Boussinesq hypothesis for the buoyancy effects. Th e convective-diffusive fluxes at the volume boundaries were represented usi ng the unified finite approach exponential-type scheme (UNIFAES), with the power-law approximation to reduce the computing time. The conditions establ ished by Rivas (1972) for the order of accuracy of the differencing scheme to be maintained in irregular grids allowed reliable accuracy estimates to be obtained. The steady-state regime was studied for Peclet numbers 1, 10, and 100; Rayleigh numbers between 1 and 2000; and cavity aspect ratios 0, 0 .5, 1, and 2. Tabulated results for average Nusselt number and maximum and minimum stream function values are reported for the cases simulated. Maps o f streamlines and isothermal lines are presented. For deep, cavities, multi ple steady-state solutions are reported.