Thermally developing flow inside a porous-filled channel in the presence of internal heat generation under local thermal non-equilibrium condition: A perturbation analysis

In the present work, a perturbation analysis is performed to study the thermally developing forced convection heat transfer inside a channel filled with a porous material under local thermal non-equilibrium (LTNE) condition. Internal heat generations within the solid and fluid phases are considered. Channel walls are subjected to a constant heat flux. It is assumed that there is a small temperature difference between the fluid and the solid phases of the porous material. So, performing a perturbation analysis enables us to avoid utilizing models for the constant wall heat flux boundary condition to investigate the hydrothermal behavior of the system. Therefore, analytical solutions are developed for temperature difference between the solid and the fluid phases as well as the local Nusselt number in the porous medium. Effects of pertinent parameters such as dimensionless axial length, Biot number, effective thermal conductivity ratio and dimensionless heat generation parameters on the Nusselt number are discussed. To further clarify the validity of the solution provided, the obtained results are compared with the solutions for two primary approaches (Models A and B) for the constant wall heat flux boundary condition. Results show that both the Nusselt number and the thermal entry length increase with the increase of thermal conductivity ratio. The Nusselt number and the thermal entry length are found to decrease with the increase of the internal heat generation of the solid phase. It is further observed that the Nusselt number and the thermal entry length are less sensitive to the solid internal heat generation at high Biot numbers. Finally, it is found that when the effective thermal conductivity ratio tends to infinity, the thermal entry length tends to zero for high Biot numbers.