Modeling and simulation of suction-driven flow and heat transfer with temperature-dependent thermal conductivity in a porous channel

In this paper, the heat transfer equation is coupled to the Navier-Stokes equations for a steady flow induced by uniform suction on two porous walls kept at different temperatures. The incompressibility of the fluid and the fact that the velocity field has two components lead to introduce the stream function in the governing equations. A similarity method is used in order to transform the resulting set of partial differential equations satisfied by the stream function and temperature into two ordinary differential equations for the same problem. The analysis is focused on the description of the behaviors of the normal and axial velocities, the streamlines, and temperature through multiple solution branches under different values of the main control parameters of the problem which are the Reynolds number, the Péclet number and the sensitivity of the thermal conductivity to the variations of temperature.