Flow and heat transfer study of an annulus partially filled with metallic foam on two wall surfaces subject to asymmetrical heat fluxes

The current research deals with the fully developed forced convection through metallic foam partly filled annulus. A metallic foam was adhered to inner and outer walls of the annulus in such a way that two foam regions and one open region were formed against the fluid flow. The inner and outer surfaces were exposed to an asymmetric heat flux ratio. To couple heat transfer and flow of the foam and open regions, no-slip coupling conditions were considered at the fluid–solid interface. Based on the fully developed fluid flow assumption, momentum, continuity, and energy equations for foam and open regions were simplified to ordinary differential equations and solved numerically as the governing equations. The impact of porosity, pore density, ratio of fluid–solid conductivity, Re number, heat flux ratio on velocity profiles, temperature distributions, flow heterogeneity, friction factor, Nu, and system performance in an annulus partly included with metallic foam were obtained. The obtained results indicated that flow heterogeneity, friction factor, and Nu depend crucially on thickness of the foam, porosity, and pore density. The study found that partially filled cases had lower performance than the empty annulus across various porosity, pore density, and Re number for a fixed conductivity ratio of 0.01, but the performance depended on the conductivity ratio. When k_r values were below 0.002, the partially filled annulus outperformed the empty one, but for a fully filled annulus, this critical k_r increased to 0.006.