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

Abstract

In this work, the finite element method was used to 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. Taking into account that this is a conjugate problem, where the temperature fields of both the porous medium and the wall are unknown, there are two well-known asymptotic limits in the literature that allow us to obtain the solution for this problem: the first one is the thermally thick wall limit , which has been widely studied previously by other authors; the second one is the thermally thin wall 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 Br ≥ 0.1, a notable temperature increase occurs in the system, which offers interesting results that have not been reported in the literature yet, because from χ = 0.6 (Br = 0.1), 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 η = 0 with respect to the temperature value at η = 1. This situation becomes more evident as the Brinkman number increases; for example, for Br = 1, the temperature in the center of the microchannel increases up to 23% with respect to the fluid temperature at the wall. Finally, the decrease of the Darcy number does not have a considerable effect on the temperature profiles.