ABSTRACT

The linear stability analysis of Marangoni convection in a composite system comprised of an incompressible fluid-saturated porous layer underlying a layer of the same fluid is considered. The upper fluid surface, free to the atmosphere, is considered to be deformable and subjected to temperature-dependent surface tension. The fluid flow in the porous layer is governed by the Forchheimer-extended-Darcy equation, and both Beavers-Joseph and Jones conditions are employed at the interface between the two layers. The resulting eigenvalue problem is solved exactly and also by the regular perturbation technique when the boundaries of the system are insulated to temperature perturbations. The effect of the crispation number, Bond number, and the other physical parameters involved therein are analyzed for the stability of the system. It is found that a decrease in the crispation number and an increase in the Bond number delay the onset of convection. Also, the effect of the ratio of the fluid to the porous layer thickness along with the other physical parameters on the control (suppress or augment) of convection is analyzed in detail.