Effect of non-uniform basic temperature gradients on Marangoni convection with a boundary slab of finite conductivity
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Date
2011-07-12T08:55:02Z
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Abstract
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.
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Effect of non-uniform basic temperature gradients on Marangoni convection with a boundary slab of finite conductivity, International Journal of Engineering Science and Technology, Shivakumara, Suma, Gangadharaiah, Linear stability, , Marangoni convection, depth ratio