Local Thermal Non-equilibrium and Heterogeneity Effects on the Onset of Double-Diffusive Convection in an Internally Heated and Soluted Porous Medium

Abstract

The effect of local thermal non-equilibrium on the onset of double-diffusive convection in a porous medium consisting of two horizontal layers, each internally heated, is studied analytically. Linear stability theory is applied. Variations of permeability, fluid thermal conductivity, solid thermal conductivity, heat source strength in the solid and fluid phases, concentration source strength, interphase heat transfer coefficient and porosity are considered. In addition to the major effects from heterogeneity of permeability, fluid thermal conductivity and heat source strength in the fluid phase as with single-diffusive convection, it is now found that major effects arise from heterogeneity of solutal source strength and porosity. We used two different methods to obtain our results. Analytical results that readily show the effects of parameter variations were obtained by using a low-term Galerkin approximation, which was validated by using a highly accurate numerical solver. Since for a problem with large number of parameters simple analytical results are highly desirable, the quantification of the accuracy of a low-term Galerkin approximation presented in our paper is quite important.