Application of the heat-balance integral to an inverse Stefan problem

Most phase change process controls are concerned with the inverse Stefan problem. In this paper, the heat-balance integral method is applied effectively to analyze the one-region and two-region inverse Stefan problems in Cartesian and spherical coordinates. It is shown that if the movement of the phase change boundary is specified arbitrarily the present technique to predict both the temperature and its gradient at the fixed boundary is simple and accurate. As numerical illustrations, the one-dimensional inward solidification problem in Cartesian and spherical coordinates are solved and discussed in detail when the movement of the phase change interface is specified as a power function. The accuracy of these approximate solutions, based on the heat-balance integral method, is demonstrated satisfyingly by comparison with the available exact and/or numerical solutions for the one-region and the two-region problems.