Analysis of non-Darcy forced convection heat transfer in a porous circular duct under LTNE condition

The heat transfer performance of non-Darcy forced convection in a fluid-saturated porous tube under local thermal non-equilibrium was numerically simulated. Firstly, the Brinkman flow model and the local thermal non-equilibrium (LTNE) model were employed to establish the mathematical model of the studied problem to predict the forced convective heat transfer. Then, the mathematical model was numerically solved using COMSOL Multiphysics simulation software. And the fluid velocity field, the solid temperature field, the fluid temperature field, and the Nusselt number were obtained. Moreover, the dependences of the Nusselt number ($Nu$) on some key parameters were analyzed in detail. It was found that the Nusselt number increases first and then tends to approach an asymptotic value with the increase of the Darcy number ($Da$) and the Biot number ($Bi$). The Nusselt number monotonously increases with increasing the Péclet number ($Pe$). On the contrary, the Nusselt number decreases first and then tends to be an asymptotic value owing to the increase of the ratio of effective thermal conductivity of fluid to effective thermal conductivity of solid (the thermal conductivity ratio $\kappa $) and ratio of effective dynamic viscosity of fluid to actual dynamic viscosity (the viscosity ratio M). The model and numerical results obtained can not only be used to improve the heat transfer capacity of porous medium pipes in engineering, but also provide references for related experiments and analytical studies.