Analytic Solutions to the Heat Equation Involving a Moving Boundary with Applications to the Change of Phase Problem (the Inverse Stefan Problem)

Long time analytic solutions to the inverse Stefan problem are presented in Cartesian and spherical coordinates. This problem deals with the phase change of a substance with the boundary conditions specified at the moving boundary. The solutions, expressed in infinite series, facilitate the calculation of temperature and heat flux variations in the phase changing medium and at the interface with the heat source element. Applications of the present analysis are in aerospace engineering, e.g., controlled ablation of thermal shields; metallurgy, e.g., controlled casting; bioengineering, e.g., cryopreservation of tissues, and numerous applications in which a controlled change of phase of a substance is involved.