Thermal and hydrodynamic behavior of forced convection gaseous slip flow in a Kelvin cell metal foam

Porous metallic foams are a key material in numerous thermal and hydraulic applications. Gas flows in such micro/nanoporous systems deviate from classical continuum descriptions due to nonequilibrium in gas dynamics, and the resulted heat and mass transport show variation by rarefaction. This study performed a wide range of pore-level analysis of convective gas flows in a Kelvin cell model at different porosities and working conditions. Rarefaction effects onto permeability and heat transfer coefficients were calculated through Darcy to Forchheimer flow regimes. Permeability increased up to 60% by increasing rarefaction while this enhancement decreased by increasing porosity. At the same time, rarefaction lessened inertial effects such that Forchheimer coefficients decreased substantially. At high flow velocities, the increase in rarefaction considerably decreased the effect of drag forces. Hence, hydrodynamic enhancement due to rarefaction was found to increase by increasing Reynolds number. On the other hand, positive influence of boundary slip and negative influence of temperature jump developing between gas and solid almost canceled each other for the studied low heat flux region of highly conductive metal foam structures. Hence, Nusselt numbers were found mostly related to Reynolds number independent from rarefaction. We described Nusselt value based on power law model as a function of Reynolds and porosity. Results and the proposed model are important to accurately predict the thermal and hydrodynamic performance of metal foams in the 80 PPI range.