In the present study, the forced convection in an axisymmetric channel has been investigated numerically. The channel, which contains different porous layers, has variable cross sectional areas along the axis. The governing equations for non-Darcy porous media are solved for the uniform inlet velocity profile and uniform inlet temperature. The walls are kept at a constant temperature. The porous medium at the middle of the channel has internal heat generation. This kind of solution domain is aimed to model the phenomena in the porous burners. The fmite element method is employed to solve the governing equations. First, the code is compared for the fully developed flow in the parallel channel. For this purpose the maximum velocities at the channel axis and the Nusselt numbers at the wall are compared with the literature. Having obtained the validated results for the code, it is applied to the problem described above. The results will be presented in terms of velocity and temperature profiles.