Influence of the interfacial internal energy on the thermocapillary steady flow

Two-dimensional creeping motion of a two immiscible viscous heat-conducting fluids on the interface for which the surface tension depends linearly on the temperature is investigated. On solid walls the temperature has extreme values and this agrees well with the velocity field of the Hiemenz's type. At small Marangoni numbers an exact solution of arising inverse boundary value problem is found. The estimation of degree of influence of the interfacial internal energy on the stationary flow is given.