Heat Transfer Complicated by Phase Transitions in a Moving Layer

A mathematical model of heat transfer that is complicated by phase transitions in a moving layer is proposed. An analytical solution is obtained using fractional differential-integral calculus. An expression for the temperature in the front as a function of the phase-transition boundary velocity is derived, from which an expression for the front velocity is found. The theoretical expression of the front velocity fits experimental data. A method for estimating the activation energy is proposed.