A Local Thermal Non-Equilibrium Analysis of Forced Convective Heat Transfer in a Metal Foam Filled Channel

A two energy equation model based on the effective porosity concept has been introduced to attack the local thermal non-equilibrium problem of forced convection in a metal foam filled channel. Non-thermal equilibrium profiles of air and solid temperatures across the channel are sought solving the set of the energy equations in which both tortuosity and thermal dispersion neglected in most of previous analyses are properly and fully accounted for. Exact solutions are found, assuming a plug flow, for the two cases of thermally fully developed convective flows through a channel, namely, the case of isothermal hot and cold walls and the case of constant heat flux walls. The resulting temperature profiles across the channel for the case of metal foam and air combination reveals that the local thermal equilibrium assumption may hold for the case of isothermal walls, but, may fail for the case of constant heat flux walls. Thus, the two energy equation model must be used for such thermal problems.