Simultaneous imbibition-heat convection process in a non-Darcian porous medium

In the present work, the nonisothermal imbibition process in a porous medium was numerically analyzed using a non-Darcian model for the momentum equation and energy equations for the wetting and dry zones. In order to show the thermal character of the problem, we assume initially that the porous medium is found at a uniform temperature T₀ and suddenly begins the imbibition process into the porous medium with a penetrating fluid at temperature T₁. The physical influence of nondimensional parameters such as Peclet number, Pe, effective heat capacity number, β_w, porous Reynolds number, Re_p, and the inertial coefficient of the porous medium, F, serve us to evaluate the position and velocity of the imbibition front as well as temperature profiles in both zones. In particular, for values of Re_pF/β_w≫1, we recover a type of nonisothermal Washburn law. The numerical predictions show that the imbibition front and the temperature fields strongly depend on the above nondimensional parameters, revealing a clear deviation of the simple Washburn law.