ABSTRACT
This chapter reviews the mathematical formulation of phase change problems and then discusses the numerical methods of solution of one-dimensional cases, with both the variable time step and the enthalpy methods. It describes some methods for a purely diffusive problem, and also presents a formulation for a diffusive–convective problem, using the finite volume methodology. The chapter illustrates the mathematical formulation of phase change problems involving solidification or melting, and considers the following one-dimensional solidification problem. The mathematical formulation of phase change problems considered previously consisted of transient heat conduction equations for the solid and liquid phases, an interface energy balance equation, and appropriate boundary and initial conditions. In many industrial problems, phase change occurs over a temperature range rather than at a specified temperature. The so-called enthalpy method has been used to solve phase change problems for such situations as well as for those dealing with a single phase-change temperature.
