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Effect of non-uniform basic temperature gradients on Marangoni convection with a boundary slab of finite conductivity
(2011-07-12T08:55:02Z) Shivakumara, I. S; Suma, S. P; Gangadharaiah, Y. H
The linear stability analysis of Marangoni convection in a fluid layer with a boundary slab of finite conductivity is considered. The effects of various non uniform temperature gradients are investigated. The lower boundary is a considered to be a thin slab of finite conductivity instead of a regular rigid surface. At the contact surface between the thin slab and the fluid layer the thermal boundary conditions are used and the upper surface is considered to be free and insulating to temperature perturbation and also surface tension effects are allowed. The resulting eigen value problem is solved exactly. The critical values of the Marangoni numbers for the onset of Marangoni convection are calculated for different temperature profile and the latter is found to be critically dependent on the depth ratio and conductivity ratio. The effects of the thermal conductivity and the thickness of the solid plate on the onset of convective instability with different temperature profile are studied in detail.