Analysis of thermally developing forced convection heat transfer in a porous medium under local thermal non-equilibrium condition: A circular tube with asymmetric entrance temperature

Thermally developing forced convective heat transfer in a circular tube filled with a fluid-saturated porous medium is analytically investigated under local thermal non-equilibrium (LTNE) condition. In this study, we assume the forced convection within the porous medium obeys Darcy's law, the tube has a constant temperature wall and possess an entrance with variable circumferential temperature distribution. Under these conditions, closed-form exact solutions of the fluid and solid phases temperatures are derived by using the method of separation of variables. The finite element (FE) analysis software COMSOL Multiphysics is employed to numerically model the studied problem. The good agreement between the presented analytical solutions and the FE solutions verifies the validity of the analytical solutions presented. Meanwhile, the consistency of the axisymmetric analytical solutions in the case of uniform entrance temperature with the existing analytical solutions in the literature confirms again the correctness and the reliability of the presented analytical solutions. Given the entrance temperature can be an arbitrary well-defined function, the presented analytical solutions are of general applicability. The subsequent parametric studies are carried out based on the presented analytical solutions. It is demonstrated that the temperature fields are non-axisymmetrical with respect to the circumferential coordinate, which is induced by the asymmetric entrance temperature. Besides, the Péclet number and the Biot number play significant roles in heat transfer. The increase of the Péclet number will result in the transition of thermally developing forced convection to the fully developed regime, while the temperature difference between the fluid and solid phases decreases with increasing the Biot number. Moreover, as a limiting case, the LTNE model degenerates to the LTE model when the Biot number approaches infinity. Our findings are of benefit to provide deep insights into the thermal behavior of forced convection in a porous circular tube with asymmetric entrance temperature under LTNE condition.