A Two-Temperature Model for the Analysis of Passive Thermal Control Systems for Electronics

Passive control of unsteady thermal loads using phase change materials is being explored for a variety of military and consumer electronics applications. The phase change materials usually have very low thermal conductivity. To enhance the thermal response of the system, thermal conductivity enhancers like metal foams, internal fins and metal filler particles have been proposed. Local thermal equilibrium between the solid matrix and the fluid is not ensured in such systems since the thermal conductivities and heat capacities for the fluid and solid are very different. The use of a single volume-averaged energy equation for both the phases cannot be justified in such situations. A two-medium approach is developed in the present work to account for the local thermal non-equilibrium. Separate energy equations are written for the solid and fluid respectively, and are closed using a steady-state interstitial heat transfer coefficient between the two phases. A general momentum equation which includes the Brinkman-Forchheimer extension to Darcy flow is employed. The resulting equations are solved using a finite volume scheme. The influence of various parameters such as the ratios of fluid to solid conductivities and heat capacities, porosity, Rayleigh number, Prandtl number, and Darcy number on the thermal and flow fields is investigated. The importance of using a two-medium approach for such situations is illustrated using the results obtained.