a b s t r a c tThe paper deals with the criterion for the onset of surface tension-driven convection in the presence of temperature gradients in a two-layer system comprising a fluid saturated anisotropic porous layer over which lies a layer of fluid. The lower rigid surface is assumed to be insulated to temperature perturbations, while at the upper non-deformable free surface a general thermal condition is invoked. Both the Beavers-Joseph and the Jones conditions have been used at the interface to know their preference and prominence in the study of the problem. The resulting eigenvalue problem is solved exactly and also by regular perturbation technique when both the boundaries are insulating to temperature perturbations. It is found that the depth of the relative layers, mechanical and thermal anisotropy parameters have a profound effect on the stability of the system. Decreasing the mechanical anisotropy parameter and increasing the thermal anisotropy parameter leads to stabilization of the system. Besides, the possibility of control of Marangoni convection by suitable choice of physical parameters is discussed in detail.

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 frictiondue 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, Λ, is less than unity and the elasticity parameter, Γ, exceeds a threshold. Further, the effects of the viscoelastic parameters and the thermal nonequilibrium on the onset of convection are analyzed in detail.PACS No.: 47.55.–pb

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