Mathematical model of the kinetics of phase transitions at the heating of the surface of a cylindrical object

If due to heating or cooling of a single-component object, a phase transition occurs, the propagation of heat significantly changes. When passing through the liquidus temperature, enthalpy, density and thermal conductivity as a function of temperature undergo discontinuity. By heating the surface of the solid metal cylindrical object above its melting temperature, the liquid phase occurs at the surface, and the corresponding phase boundary moves to the cylinder axis. The article presents the derivation of heat propagation equations in the body, taking into account, in addition to the phase transition, the change in the size of parts of the body due to density dependence on temperature. To the resulting system of equations, straightening fronts method was applied: such coordinates have been entered that for which interface surface is stationary. The resulting system of differential equations is reduced to finite-difference equations. A computer program was developed to solve the resulting system of difference equations. Results of one of such calculations are given in the article. The developed method allows to calculate the velocity of the phase boundary, as well as the object temperature at any point and at any time. The results may be interesting not only for metallurgists, but also in metrology to develop self-testing temperature sensor theory.