Effect of nonuniform temperature gradientson thermogravitational convectionin aporouslayer using a thermal nonequilibrium model

The effect of various forms of nonuniform basic temperature gradients on the onset of convection in a Newtonian fluidsaturated isotropic porous layer is investigated when the fluid and solid phases are not in local thermal equilibrium. A two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation and the Forchheimer-extended Darcy model is used to describe the flow. The eigenvalue problem is solved numerically using the Galerkin technique. Comparisons are also made of the critical stability parameters between the present results and published ones for the linear basic temperature profile case, and the agreement is found to be good. The possibility of delaying or hastening the onset of convection by the basic state temperature gradients along with the influence of parameters representing the local thermal non-equilibrium effect is analyzed in detail. When compared with the nonuniform temperature gradients, it is found that the linear temperature profile indicates a reinforcement of stability. In addition, the role of thermal depth on the critical conditions is assessed in the case of piecewise linear temperature profiles.