Integral formulation of solutions of boundary-value problems of heat and mass transfer in domains with moving boundaries

Abstract

Using the Fourier transform, integral representations of solutions to boundary value problems of heat conduction and diffusion in a two-phase region with a moving interface are obtained. The proposed approach makes it possible to obtain the equation of motion of the interface without the need to first find the temperature and (or) concentration fields. This makes it possible to study the stability of the interface with respect to disturbances in its shape. The validity of the proposed approach is demonstrated by the example of self-similar growth of a spherical crystal in a supercooled melt and crystallization of the melt on a substrate of the same substance. On the basis of the obtained equation, which determines the rate of self-similar motion of the interface, the features of the kinetics of crystallization of the melt on the substrate are analyzed. The conditions of applicability of the developed approach to the solution of boundary value problems of heat conduction and diffusion in regions separated by a moving boundary are briefly discussed.