FORCED CONVECTION OF A FLUID WITH TEMPERATURE-DEPENDENT VISCOSITY FLOWING THROUGH A POROUS MEDIUM CHANNEL

Abstract

Several contemporaneous applications, such as cooling of military avionics and porous journal bearings, involve the flow of fluids with temperature-dependent viscosity through a heated/cooled porous channel. Although practical and fundamental, this apparently simple problem has not yet been considered in the literature. This study focuses on the convection effect of a fluid, with temperature-dependent viscosity, flowing through a heated (uniform wall heat flux) porous channel. Results show a surprisingly small effect on the Nusselt number, notwithstanding the strong effect the viscosity variation is shown to have on the flow (e.g., local velocity distribution). This is contrary to what has been observed in the case of convection along a single surface where the viscosity dependency on temperature strongly affects the heat transfer coefficient (i.e., Nusselt number). This contrast is because of the omission, in the previous analysis, of the form drag effects from the flow equation. Our results show also that the departure from the uniform-viscosity behavior is only for a short distance along the channel and is inversely proportional to the wall heat flux. Finally, a comparison between the mechanical power for pumping the fluid through the channel and the thermal energy necessary for heating the fluid is presented.