A numerical study is reported on the fully developed unsteady laminar fluid flow in microchannel parallel-plates partially filled with a uniform porous medium and partially filled with a clear fluid. The flow is induced by the movement of one of the plates and the pressure gradient. The Brinkman-extended Darcy model is utilized to model the flow in the porous region, while the Stokes equation is used in the clear fluid region. A theoretical analysis is also presented for the fully developed steady flow to find closedform expressions for the interfacial velocity and the velocity and skin frictions at the bounding plates. Numerical computations shows excellent agreement between the closedform solutions for fully developed steady flow and the numerical solution to unsteady flow at large values of time.