Comparison of Computational and Quasi-Static Solutions of Phase Change With Heat Generation

Abstract

In this paper, we investigate the effects that the volumetric heat generation has on the movement and steady-state location of a solid-liquid phase change front in melting and freezing processes. Volumetric heat generation enhances melting and impedes freezing. This phenomenon occurs in nuclear, geologic, cryogenic and material processing applications. We compare the results from a FLUENT computational model with analytical results of a quasi-static solution of the governing equations. These models are applied for constant surface temperature boundary conditions and various volumetric heat generation values in cylindrical plane wall and spherical geometries. The quasi-static method results in an exact steady-state solution which shows that the location of the phase change front is inversely proportional to the square root of the volumetric heat generation. This method is valid for Stefan numbers less than one and the computational results for this regime give excellent agreement with the analytical model, thereby validating the technique and solutions. For the sake of comparison, we also plot the analytical model and computational results for Stefan numbers of one and greater. The quasi-static analytical solution converges more rapidly to the steady-state value than the computational solution. As expected, at longer time intervals, both the analytical and computational solutions converge to the exact steady-state solution.