Abstract: On the basis of the developed three-dimensional non-stationary model of motion, calculations of heat transfer in a
moving roll were carried out. In this case, the action of all the main physical factors during their interaction was taken into account:
diffusion and convective heat transfer, the dependence of viscosity on temperature, the thermocapillary effect, the appearance and
evolution of surface deformations. it was found that the size of the heater significantly affects the temperature fields and surface
deformations, as well as the value of temperature extremes. An analytical formula is derived for calculating the maximum
temperature rise attainable on the substrate of its average value.
Index terms: heat transfer modeling, thin films, numerical calculations, surface deformation.