Analysis of Constant-Heat-Flux Heat Transfer in Metal Foam

The use of open-cell metal foam in contemporary heat exchange technologies is increasing rapidly. The high surface area density of metal foam places them among the best options for heat exchanger core materials. Certain simplifying assumptions for the combined conduction/convection heat transfer analysis in metal foam have not been exploited. Solving the complete, and coupled, fluid flow and heat transfer governing equations numerically is time consuming. A simplified two-dimensional analytical model for the heat transfer in open-cell metal foam block subjected to constant heat flux, and cooled by a low-conductivity fluid, is presented. The model assumes local thermal equilibrium between the solid and fluid phases in the foam, and neglects the conduction in the fluid. The local thermal equilibrium assumption is supported by previous studies performed by other workers. The velocity profile in the foam is taken as non-Darcean slug flow. An approximate solution for the temperature profile in the foam is obtained analytically. The temperature profile decays in what looks like an exponential fashion as the distance from the heat base increases, and increases in the flow direction. The model along with the simplifying assumptions were verified by direct experiment using air and an aluminum foam block heated from above by constant heat flux, for a range of Reynolds numbers. Very good agreement was found between the analytical and the experimental results.