Double‐Diffusive Convection in a Porous Medium, Nonlinear Stability, and the Brinkman Effect

Abstract

This paper establishes a nonlinear energy stability theory for the double‐diffusive convection in a porous medium when both viscosity and thermal expansion coefficient are allowed to vary with temperature. After presenting a nonlinear stability theorem, a variational problem is formulated and the numerical solutions via the compoound matrix method are carried out. It is noted that higher values of the thermal coefficient and higher values of the viscosity ratio have the effect of delaying the onset of convection.