Convective flow and heat transfer through a composite porous/fluid system have been studied numerically. The composite medium consists of a fluid layer overlaying a porous substrate, which is attached to the surface of the plate. The numerical simulations focus primarily on flows that have the boundary layer characteristics. However, the boundary layer approximation was not used. A general flow model that accounts for the effects of the impermeable boundary and inertia is used to describe the flow inside the porous region. Several important characteristics of the flow and temperature fields in the composite layer are reported. The dependence of these characteristics on the governing parameters such as the Darcy number, the inertia parameter, the Prandtl number, and the ratio of the conductivity of the porous material to that of the fluid is also documented. The results of this investigation point out a number of interesting practical applications such as in frictional drag reduction, and heat transfer retardation or enhancement of an external boundary.