Transient mixed convection in a channel with an open cavity filled with porous media

In this work transient mixed convection in a porous medium in a horizontal channel with a open cavity below is studied numerically. The cavity presents a heated wall at uniform heat flux and the other walls of the cavity and the channel are assumed adiabatic. Air flows through the horizontal channel. The heated wall of the cavity experiences a uniform heat flux in such a way that the forced flow is perpendicular to the motion due to natural convection. The study is carried out employing Brinkman-Forchheimer-extended Darcy model and two energy equations due to the local thermal non-equilibrium assumption. The flow in the channel is assumed to be two-dimensional, laminar, incompressible. Boussinesq approximation is considered. The thermophysical properties of the fluid are evaluated at the ambient temperature. The results for stream function and temperature distribution given at different times are obtained. Wall temperature value are given and also, the velocity and temperature profiles in several sections of the cavity are presented. In addition, the Nusselt number, both local and average, is presented along with the temporal variations of the average Nusselt number.