Simplified heat transfer analysis in metal foam with low-conductivity fluid

The use of open-cell metal foam in contemporary technologies is increasing rapidly. 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 analytical model for the heat transfer in open-cell metal foam 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 using a similarity transform. The solution for the temperature profile is represented by the error function, which decays in what looks like an exponential fashion as the distance from the heat base increases. The model along with the simplifying assumptions were verified by direct experiment using air and two aluminum foam samples heated from below, for a range of Reynolds numbers. Each foam sample was 5.08 cm-thick in the flow direction. One sample had a pore density of ten pores per inch while the other had twenty pores per inch. Very good agreement was found between the analytical and the experimental results for a considerable range of Reynolds number, with the agreement being generally better for higher Reynolds numbers, and for foam with higher surface area density.