Effect of magnetic field on the liquid-gas interfacial deformation in thermocapillary convection problem

Abstract.

Liquid contained in an open cavity flows owing to a temperature gradient applied along its free surface. The thermal variation of surface tension induces a steady viscous flow directed from hot end to cold end. For small aspect ratios, giving flow in thin, two dimensional slots, an asymptotic theory valid for $(A \rightarrow 0)$ is used to show that the interface undergoes an O(1) deformation from its flat position. Further, it is observed that for some values of the Hartmann number, the deformed interface can be made almost flat.