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This work introduces a new approach of analyzing convective heat transfer in porous medium by considering the foam structure as a type of fin. It provides the resulting heat transfer characteristics for the design of a longitudinally flowed tube bundle reformer used for the Micro Gas Turbine Solid Oxide Fuel Cell (MGT-SOFC) hybrid process. Owing to a limited experimental database available in literature for the above-mentioned situation, a physical model is initially introduced for a channel flow configuration between two large flat plates using a commercial PDE solver. This model is then validated with experimental results available in literature. A comparison with theoretical solutions is also conducted. Later, this model is modified/adapted for a pipe flow configuration. The physical model for a channel with representative cross-section shape of a longitudinally flowed tube bundle is more complex and is therefore built in a commercial CFD-Solver. A comparative study of the heat transfer behavior in channels of different cross-sections is performed based on a new dimensionless correlation, whose physical coherence with fin efficiency is explained and mathematically proved. The applicability of the heat transfer correlation from one cross-sectional shape to the other are discussed. The proposed new treatment of the porous medium as a fin structure considerably simplifies the heat transfer analysis in porous medium by the clear physical meaning behind fin efficiency and Biot number. This relationship contributes to a better understanding of the heat heat transfer characteristics in porous media in contrast to the correlation between Nusselt number and Reynolds number. Furthermore, this correlation enables a direct comparison between foam structures of different parameters because the fin efficiency is always between 0 and 1. The strong physical background of new correlations also enhances the reliability and plausibility at characterizing and designing the metal foam for heat transfer enhancement.

Comparison of convective heat transfer in metal foam-filled channels of three different cross-sections