Heat transfer in open-cell metal foams

The paper explores the use of open-celled metal foams as compact heat exchangers, exploiting convective cooling. An analytical model is developed for model foams with simple cubic unit cells consisting of heated slender cylinders, based on existing heat transfer data on convective crossflow through cylinder banks. A foam-filled channel having constant wall temperatures is analyzed to obtain the temperature distribution inside the channel as a function of foam density, cell size and other pertinent heat transfer parameters. Two characteristic length scales of importance to the problem are discussed: the minimum channel length required for heating the fluid to its goal temperature and the thermal entry length beyond which the transfer of heat between fluid and channel wall assumes a constant coefficient. The overall heat transfer coefficient of the heat exchanging system is calculated, and the pressure drop experienced by the fluid flow obtained. These results are used to analyze and guide the design of optimum foam structures that would maximize heat transfer per unit pumping power. Two examples are given to demonstrate the applicability of the analytical model: heat sinks for high power electronic devices and multi-layered heat exchangers for aeronautical applications. The present model perhaps oversimplifies the calculation of transport in a metal foam consisting of non-circular, possibly sharp-edged ligaments, and so likely leads to overestimates. Nevertheless the trends of heat transfer predicted by the model (for dependence on foam relative density, duct geometries, fluid velocity, etc.) are expected to be valid for a wide range of open-cell foams and are in reasonable agreement with available experimental data on aluminum foams (Bastawros and Evans, Proc. Symp. Application of Heat Transfer in Microelectronics Packaging. IMECE, Dallas, TX, 1997).