The volume averaged Navier-Stokes and energy equations with a modified Darcy model are used to simulate the flow and thermally developing heat transfer phenomena between parallel plates filled with a porous medium. Two different cases are investigated: (1) the walls at constant and equal temperature and (2) the walls at constant and equal heat flux. A fully developed velocity profile is given at the inlet of the channel where uniform temperature is set. Simulations are carried out for the range of Darcy numbers from 10(-1) to 10(-5), and porosity is set to 0.9. The finite element method is employed to solve the governing equations. Results are presented for different Darcy numbers and are given in terms of local and average Nusselt numbers. Validation studies are performed for similar cases, including porous and clear fluid media.