Optimum geometry of solid porous spheres with heat generation

Abstract

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.

Spent nuclear fuel has to be cooled so that the decay heat generated does not melt the containment system, which could lead to unintentionally release of radioactive material to the surrounding. The heat transfer mechanisms involved in the cooling have historically been analysed by assuming that the fluid and solid phases are at local thermal equilibrium (LTE) in order to simplify the analysis. An analytical model was developed to minimize the thermal resistance of an air cooled porous matrix made up of solid spheres with internal heat generation. This was done under the assumption of LTE. It was found that the predicted optimum sphere diameter and the minimum thermal resistance were both robust in that they were independent of the heat generation rate of the solid spheres. Results from the analytical model were compared to those from a commercial numerical porous model using liquid water and air for the fluid phase, and wood and silica for the solid phase. The magnitudes of the minima of both the temperature difference and the thermal resistance seem to be due to equally contribution from the thermal conduction heat transfer inside the solid spheres and heat transfer in the porous medium. Because the commercial numerical porous model models only the heat transfer occurring in the porous medium, it expectedly predicts half of the magnitudes of the minima of the temperature difference and thermal resistance of those by the analytical model.