Effect of inertia on the onset of mixed convection in a porous layer using a thermal nonequilibrium model

The article deals with the onset of mixed convection in a porous layer heated from below by considering the effect of inertia when the fluid and solid phases are not in local thermal equilibrium in the frame of a linear stability analysis. The mixed convection is considered in the sense of a mean horizontal pressure gradient. Critical Rayleigh number and wave number are analytically determined in both two-dimensional (2-D) and 3-D cases. In the 2-D case the parameters of the problem are the inertia-modified parameter G*, porosity-scaled conductivity ratio gamma, and scaled interphase heat transfer coefficient H. In the 3-D case an additional parameter occurs, namely, the angle of roll inclination alpha. The inertia effect acts as a stabilizing factor in the convection onset, and this factor dominates the effect produced by the local thermal nonequilibrium conditions.