Semi-analytical solution for fully developed forced convection in metal-foam filled tube with uniform wall temperature

Fully developed flow and heat transfer in metal-foam filled tube with uniform wall temperature(UWT) is semi-analytically investigated based on the Brinkman–Darcy model and the two-equation model, in which the inertia term, axial conduction, and thermal dispersion are ignored. A two-dimensional numerical simulation that adopts the full governing equations is also conducted to analyze the effects of neglected terms on flow and thermal transport performance by comparing with the semi-analytical solution. The effects of the relevant parameters and thermal boundary conditions including UWT and uniform heat flux(UHF) on the heat transfer characteristics are discussed based on the semi-analytical solution. The results show that the inertia term has a significant effect on the prediction of pressure drop, but has a relatively mild effect on Nusselt number. The axial conduction has significant effect on the Nusselt number at lower Reynolds number, and the effects of thermal dispersion can be neglected when the thermal conductivity ratio between fluid and solid is remarkably smaller for air/metal foam as example(kf/ks<3×10-3). The predicted Nusselt number of the semi-analytical solution is about 8% to 15% lower than that of the numerical solution with full model in the range of 4×10-5<kf/ks<3×10-3. Moreover, the temperature profile of solid is more sensitive to pore density and porosity than that of fluid under UWT condition. The Nusselt number under UWT is about 7% to 25% lower than that under UHF, and the difference is mainly determined by interfacial convection rather than solid conduction.