Problem formulation

Consider the domain which is divided into the regions and by the interface as shown in Fig. 18.

Figure 18: Domain split into and by the surface .

Figure 19: Zoom of the interface .

Knowing the initial temperature in the domain, , we seek to determine the evolution of the function which satisfies the governing equations

where is the volumetric heat capacities of the phases, and are the thermal conductivity tensors.

The above are supplemented with external boundary conditions

with and prescribed temperatures and heat fluxes, respectively.

The motion of the surface is described by a Stefan condition, written as:

where is the volumetric latent heat of fusion. This equation, in turn with the condition that the temperature equal the melting temperature on the interface

   on (27)

completes the description of the boundary value problem we wish to solve.