Stability of Marangoni Convection in a Fluid Layer with Variable Viscosity and deformable Free Surface under Free-Slip condition

Abstract

The steady marangoni convection is investigated in ahorizontal layer of fluid with a free-slip bottom heated frombelow and cooled from above. Since the viscosity is temperaturedependentthe consequences of relaxing oberbeck-boussinesqapproximation and free surface deformability are theoreticallyexamined by means of small disturbance analysis. Prediction forthe onset of convection are obtained from the analysis bynumerical technique. The effect of variable viscosity and surfacedeformation on the onset of fluid motion is investigated in detail.It is shown that the critical values of marangoni and wavenumber depend strongly on the viscosity variation and surfacedeformation.

Keywords

• Marangoni convection: Heat generation
• Free-slip