Stefan Problem with Internal Heat Generation: Comparison of Numerical Modeling and Analytical Solution

The Stefan problem with internal heat generation can be found in various industrial applications. In particular, this problem describes melting of nuclear fuel rods during a reactor emergency. The present study reports on numerical modeling of the heat conduction equation and the Stefan equation with an application of the method of catching of the front into a space grid node. To solve numerically the heat conduction equation we realized an implicit four-node scheme using the Thomas method and iteration procedure.