Freezing and Melting of Materials With Variable Properties and Arbitrary Heat Fluxes
A solution is presented to the problem of phase changes in a semi-infinite region of liquid or solid with variable thermal properties and arbitrary heat fluxes. The phase change is caused by sudden exposure of the surface to a heat flux. The heat balance integral method is used to reduce the complicated boundary value problem involving a nonlinear differential equation and a nonlinear boundary condition to a system of simultaneous algebraic equations involving the surface temperature and the melting line location. Numerical results based on the governing equations are presented in graphic form for melting of solids in which the heat fluxes are linear or exponential functions of time and the thermal properties are linear functions of temperature. Results with constant thermal properties are also included for comparison purposes. The formulation for solidification is equally applicable to the case of melting only when the thermal properties are assumed constant.
Chung, Benjamin T.F. and Yeh, L. T., "Freezing and Melting of Materials With Variable Properties and Arbitrary Heat Fluxes" (1976). Mechanical Engineering Faculty Research. 1027.