Multiple Solutions of Double-Diffusive Convection in Porous Media due to Opposing Heat and Mass Fluxes on Vertical Walls

Abstract

The double-diffusive convection in a porous medium due to the opposing heat and mass fluxes on the vertical walls is solved analytically. In the former analysis, we investigated only when ω < π, the parameter arising from a combination among the density stratification and the buoyancy effects. However, it is shown in the present research that a solution is also possible when ω > π. The Sherwood number Sh is shown to decrease monotonically with an increase in the buoyancy ratio N when ω > π, and Sh approaches 1 when N is 1. We define N_min as the minimum value of N when Ω is imaginary and ω = π. N_min increases with an increase in R_c. However, N_min approaches a constant as Le increases. Furthermore, although the convection pattern is mainly temperature-driven, concentration-driven convection cells also exist under certain.