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 binary mixture with a common interface in a layer bounded by solid walls is studied. A radial time-varying temperature distribution is specified on the lower substrate; the upper wall is assumed to be thermally insulated. Assuming a small Marangoni number, the structure of a steady-state flow is described depending on the layer thickness ratio and taking into account the influence of mass forces. The solution of the nonstationary problem is determined in Laplace transforms by quadratures. It is shown that if the given temperature on the lower substrate stabilizes over time, then with increasing time the solution reaches the resulting steady-state mode only under certain conditions on the initial distribution of concentrations in the mixture.