Similarity Solution of Freezing or Melting Processes with Variable Thermal Properties
Freezing or melting processes, using substances with variable thermal properties, taking place in a body with variable cross-sectional area, are considered. The method of obtaining the similarity solution involves three steps, 1) transformation of the position coordinate, 2) description of the temperature field, and 3) consideration of the temperature distribution in the neighbourhood of the phase boundary. It reduces the system of equations in the neighbourhood of the phase boundary to one that is independent of the cross-sectional area. The solution of this system is a universal function and is applicable to bodies with different cross-sectional areas. A theorem for calculating the rate of propagation of the phase boundary in a body of variable cross-sectional area from that in a body of constant cross-sectional area is obtained.