Modeling of Conduction and Natural Convection in Ice-Water Systems Containing Porous Metal Foams

Mathematical models and numerical predictions of heat conduction and laminar natural convection in ice-water systems containing porous metal foams are presented, in the context of computationally convenient two-dimensional steady-state problems with rectangular calculation domains. The Darcy-Brinkman-Forchheimer equations were used to model momentum transfer in the liquid-water-metal-foam region. For modeling the heat transfer, volume-averaged equations governing two intrinsic-phase-average temperature fields were used: one for the metal foam and the other for the water (solid or liquid). The following improvements are proposed: novel expressions for the interfacial (metal-water) heat transfer coefficient in both the convection and conduction regimes; and effective thermal conductivity correlations that provide consistency between the formulations of one-temperature and two-temperature models in the limit of local thermal equilibrium. A well-established fixed-grid, co-located, finite volume method (FVM) was adapted and used for the numerical solutions. The proposed models and FVM were used to solve the test and demonstration problems involving conduction and laminar natural convection in ice-water-aluminum-foam systems contained in rectangular enclosures. The findings and results of these investigations are presented and discussed in this paper.