The Structure of a Two-Layer Flow in a Channel with Radial Heating of the Lower Substrate for Small Marangoni Numbers

The three-dimensional flow of a system of a viscous heat-conducting fluid and a binarymixture with a common interface in a layer bounded by solid walls is studied. A radialtime-varying temperature distribution is specified on the lower substrate; the upper wall isassumed to be thermally insulated. Assuming a small Marangoni number, the structure ofa steady-state flow is described depending on the layer thickness ratio and taking into account theinfluence of mass forces. The solution of the nonstationary problem is determined in Laplacetransforms by quadratures. It is shown that if the given temperature on the lower substratestabilizes over time, then with increasing time the solution reaches the resulting steady-state modeonly under certain conditions on the initial distribution of concentrations in the mixture.