Influence of the wicking process on the heat transfer in a homogeneous porous medium

In this work, we analyze 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 found initially at temperature T₀ and pressure P₀; suddenly the lower part of the porous medium touches a liquid reservoir with temperature T₁ and pressure P₀ and begins the spontaneous wicking process into the porous medium. The physical influence of two nondimensional parameters such as the ratio of the characteristic thermal time to the characteristic wicking time, β and α 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 position and velocity of the wicking front as well as the temperature profiles and the corresponding Nusselt numbers in the wetting zone. In particular, for small values of time we recover the well-known Washburn law. The numerical predictions show that the wicking and the temperature profiles depend on the above nondimensional parameters, revealing a clear deviation of the simple Washburn law.