Steady thermocapillary flows in two-dimensional slots

Liquid in a slot flows owing to a temperature gradient applied along its free surface. The thermal variation of surface tension induces a steady viscous flow directed on the surface from hot to cold, and recirculating below. For small aspect ratios A, giving flow in thin, two-dimensional slots, an asymptotic theory valid for A -> 0 is used to obtain the fluid and thermal fields as well as the interfacial shapes. Solutions are obtained for both fixed lines and fixed angles at the contact between the interface and the solid side walls.