A Study of the Thermal Diffusion Equation with Boundary Conditions corresponding to Solidification or Melting of Materials Initially at the Fusion Temperature

Abstract

Solutions are presented for determining the position of the solid-liquid interface and the temperature-time history of the surface of solidifying or melting materials initially at the fusion temperature. These solutions include treatment of the cylinder, the sphere and the semi-infinite solid. Solutions were obtained by analytical methods and by means of an electrical analogy to the thermal system. The application of the electrical analogy to the solution of problems in solidification is described.