The transient hydrodynamics behavior of the fluid flow in parallel-plate channels partially filled with porous material is investigated numerically. The role of the local macroscopic inertial term in the porous domain momentum equation is studied. It is found that the effect of the local inertial term on the channel hydrodynamics behavior is insignificant when Da < 1 x 10(-6), over the entire range of 0.1 < mu (R) < 10, 0 < A < 10(4), and for all porous substrate thicknesses. Also, it is found that the deviation between the predictions of the transient and the quasi-steady models is more significant in the porous domain and the deviation decreases as the time proceeds. <(c)> 2001 Elsevier Science Ltd. All rights reserved.