A detailed investigation of the forced convective cooling of a heated obstacle mounted upon a channel wall is presented. The Navier-Stokes equations are used to characterize the flow field surrounding the conductive obstacle. Special emphasis is given in the systematic analysis to detail the local Nusselt number distributions and mean Nusselt numbers for the individual exposed obstacle faces. The study employs parametric variations in the obstacle height and width, as well as the thermal conductivity ratio k(solid)/k(fluid), flow rate (Re-Dh), and heating method, to detail important fundamental and practical results. Comparison with an analytical solution for thermally developing flow in a channel shows reasonable estimates to Nusselt numbers can be made by choosing an appropriate length scale. It is shown that specific choices in obstacle size, shape and thermal conductivity can produce significant effects on the flow and heat transfer characteristics.