Analytical solution of forced convective heat transfer in parallel-plate channel partially filled with metallic foams

The forced convection flow and heat transfer characteristics in parallel-plate channel partially filled with metallic foams have been studied analytically. To predict fluid and thermal transport in the bottom heated partially filled channel, the Brinkman-extended Darcy momentum model and Non-equilibrium heat transfer model for porous media were employed for the foam filled region coupling with the momentum and energy conservation equations for foam free region. The interface between foam filled region and foam free region are subject to continuous temperature and energy balance to derive the analytical solutions for fully developed flow and convection heat transfer in entire plate channel including foam filled region and non-foam region. Then, the velocity and temperature distributions were predicted for the whole region of the parallel-plate channel based on the analytical solutions. The effects of key parameters on flow resistance and heat transfer performance has been investigated. Unlike the completely filled channel, the influences of pore density and porosity on flow and heat transport are dependent on the height of the foam.