Studying influence of the wicking process on the heat transfer in a homogeneous inclined porous medium

Abstract

In this research, we study the spontaneous wicking process of a fluid in a homogeneous porous medium taking into account that the medium is subject to the presence of a temperature gradient, including the gravity effects. We assume that the porous medium is initially at temperature $T_0$ and pressure $P_0$ ; then the lower part of the porous medium faces a liquid reservoir with temperature $T_1$ and pressure $P_0$ and begins the spontaneous wicking process into the porous medium. The physical influence of two nondimensional parameters like the ratio of the characteristic thermal time to the characteristic wicking time, $\beta$ and $\alpha$ are defined as the ratio of the hydrostatic head of the imbibed fluid to the characteristic pressure difference between the wicking front and the dry zone of the porous medium, serves us to evaluate the velocity of the wicking front as well as the temperature profiles and the corresponding Nusselt numbers in the wetting zone. Influence of the heat dissipation and slope of porous medium on temperature and velocity profile is studied. In particular, for small values of time the well-known Washburn law is recovered. The numerical predictions show that the the velocity and temperature profiles depend on the above nondimensional parameters, revealing a clear deviation of the simple Washburn law.