Heat transfer analysis in a porous microchannel heat sink with variable permeability*

In this study, the heat transfer of a Newtonian fluid flowing through a porous microchannel with constant permeability and different models of variable permeability is analyzed numerically. In addition a conjugate heat transfer analysis in the microchannel walls is considered. The governing equations were solved using the finite element method under the variational approach for the momentum equation, energy conservation equation and the coupled heat conduction equation. Temperature field results were obtained at the thermally thick and thermally thin asymptotic limits in the fluid and at the thermally thin limit in the wall for visualization of longitudinal heat conduction effects. The results indicate that the temperature field is strongly influenced by the velocity field and the variable permeability function of each case studied. Also, it could be observed that the temperature varies as a function of the Brinkman number (Br), which represents the effect of viscous dissipation. However, there were no significant changes of the fluid and temperature and wall temperature profiles as a function of the Darcy number. Finally, the model in which the largest temperature difference was experienced compared to the case with constant permeability was the potential model, which had a 66.7% higher fluid temperature at the outlet and in the center of the microchannel and a 45.7% higher wall temperature, for Br= 1.0 and taking into account the longitudinal effects of heat conduction in the wall.