No abstract

Summary. The onset of Marangoni convection with throughflow in a horizontal fluid layer with upper boundary free and insulating to temperature perturbations and the lower boundary rigid and either conducting or insulating to temperature perturbations is investigated. The resulting eigenvalue problem is solved exactly. The Prandtl number arising due to throughflow plays a crucial role in determining the stability of the system. It is found that a small amount of throughflow in one particular direction destabilizes the system depending on the Prandti number and temperature boundary conditions.

Linear stability analysis has been performed to investigate the effect of internal heat generation on the criterion for the onset of Marangoni convection in a two-layer system comprising an incompressible fluid-saturated anisotropic porous layer over which lies a layer of the same fluid. The upper non-deformable free surface and the lower rigid surface are assumed to be insulated to temperature perturbations. The fluid flow in the porous layer is governed by the modified Darcy equation and the Beavers-Joseph empirical slip condition is employed at the interface between the two layers. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is also obtained by using regular perturbation technique with wave number as a perturbation parameter. The effect of internal heating in the porous layer alone exhibits more stabilizing effect on the system compared to its presence in both fluid and porous layers and the system is least stable if the internal heating is in fluid layer alone. It is found that an increase in the value of mechanical anisotropy parameter is to hasten the onset of Marangoni convection while an opposite trend is noticed with increasing thermal anisotropy parameter. Besides, the possibilities of controlling (suppress or augment) Marangoni convection is discussed in detail.

No abstract

No abstract