Fully developed forced convective heat transfer in an annulus partially filled with metallic foams: An analytical solution

An analytical solution for fully developed forced convective heat transfer in an annulus partially filled with metallic foam was proposed. The inner surface attached with an annular metallic foam layer was exposed to constant heat flux while the outer surface was adiabatic. In the metallic foam region, the Brinkman-Darcy equation was used to describe the fluid flow and the thermal non-equilibrium model was employed to establish the heat transfer equations. At the porous-fluid interface, no-slip coupling conditions were utilized to couple flow and heat transfer of the porous and open regions. A closed-form analytical solution was obtained for velocity and temperature profiles. The explicit form of friction factor and the Nusselt (Nu) number were also provided. The solutions were validated by two extreme cases: the empty annulus and the annulus fully filled with metallic foam. The effects of key parameters on friction factor, Nu number, and j/f ^1/3 were examined. The relationship between flow heterogeneity and heat transfer was also discussed by introducing the flow heterogeneity coefficient. The porosity, pore density, and foam thickness for engineering applications were recommended. In the present analytical solution, a benchmark was also established for improving discretizing schemes in numerical works.