Siberian Federal University

A steady thermocapillary flow of a viscous incompressible fluid in a flat layer on a solid substrate is investigated. The free boundary is assumed to be flat, and the surface tension coefficient depends on temperature by a power law. The original convection problem is reduced to a boundary value problem for a nonlinear system of ordinary differential equations. An exact solution is found for small Marangoni numbers. The nonlinear problem was solved numerically using the transformation method