Two-Dimensional Plane Steady-State Thermocapillary Flow

Abstract

The problem of a two-dimensional steady flow of a fluid in a flat channel with a free boundary when the surface tension coefficient depends linearly on the temperature is considered. On the channel bottom, a fixed temperature distribution is maintained. The temperature in the fluid is distributed in accordance with the quadratic law, which is consistent with the velocity field of the Xiemenz type. The arising boundary-value problem is strongly nonlinear and inverse with respect to the pressure gradient along the channel. The application of the tau-method shows that this problem has three different solutions. In the case of a thermally insulated free boundary, only one solution exists. Typical flow patterns are studied for each solution.