Perturbation solution to heat conduction in melting or solidification with heat generation

The Stefan problem involving a source term is considered in this technical note. As an example, planar solidification with time-dependent heat generation in a semi-infinite plane is solved by use of a perturbation technique. The perturbation solution is validated by reducing the problem to the case without heat generation whose exact solution is available. An application to the case with constant heat generation is presented, for which a closed-form solution is obtained. The effects of heat generation and Stefan number on the evolution of solidification are examined using the perturbation solution.