Onset of convection in a viscoelastic-fluid-saturated sparsely packed porous layer using a thermal nonequilibrium model

Abstract

A linear stability analysis is carried out to study viscoelastic fluid convection in a sparsely packed horizontal porous layer heated from below. The viscoelastic fluid flow in the porous medium is modeled by using a modified Brinkman-Lapwood-extended Darcy model with the fluid viscosity different from the effective viscosity, which accounts for the viscoelastic properties and friction due to macroscopic shear. Besides, a two-field model for temperature each representing the solid and fluid phases separately is employed. The conditions for the occurrence of direct and Hopf bifurcations of the thermal convective instability are obtained analytically. It is shown that Hopf bifurcation occurs only if the retardation to relaxation-time ratio, A, is less than unity and the elasticity parameter, ?, exceeds a threshold. Further, the effects of the viscoelastic parameters and the thermal nonequilibrium on the onset of convection are analyzed in detail. © 2006 NRC.