Effects of Internal Heat Generation on Solidification

We present solutions for solid-liquid phase change in materials that generate internal heat. This problem is solved for both cylindrical and semi-infinite geometries. The analysis assumes a temperature profile in the solid phase and constant temperature boundary conditions on the exposed surfaces. We derive differential equations governing the solidification thickness for both geometries as functions of the Stefan number and the internal heat generation (IHG). For the cylindrical geometry, the solidification layer obtains a steady-state value which is related to the inverse of the square root of the IHG. The solutions to the semi-infinite geometry problem show that when the surface is cooled to below the freezing point, a solidification layer forms along the edge and begins to grow until it reaches a maximum, then begins remelt.