Impact of viscous dissipation on the conjugate heat transfer between the walls of a porous microchannel

In this work, we study numerically the viscous dissipation that occurs when a Newtonian fluid circulates through a porous microchannel that operates as a heat sink, in which a constant heat flux is applied from the outer walls of the porous microchannel into the fluid. The temperature fields of both the porous medium and the wall are unknown, for instance, there are two well-known asymptotic limits in order to obtain the solution for this problem: the thermally thick wall limit and the the thermally thinwall limit, where the longitudinal effects of heat conduction in the microchannel wall are considerably more important than the ones occurring in the transverse direction. Therefore, in this study, we analyze the competition between these effects and viscous dissipation, as well as the influence that both have on the temperature profiles of the fluid and the wall. The results show that for a Brinkman number (Br) equal to …0.1, a notable temperature increase occurs in the system, which offers interesting results that have not been reported in the literature yet, because there is a higher temperature in the center of the microchannel than in the vicinity of the wall; that is, the fluid temperature is higher at the center of the microchannel than in the heated walls.