An extensive parametric analysis has been performed to fully investigate the fundamental aspects of laminar convective cooling of an array of heated obstacles within a channel. The analysis employs the finite element method to solve the Navier-Stokes equations for the fluid flow and fully accounts for conjugate conduction within the solid obstacles. The influences of parametric changes in the obstacle thermal conductivity, fluid coolant flow rate, and input heating method are examined to establish important fundamental effects and provide practical results. The dependence of the streamlines, isotherms, and local Nusselt numbers on the governing parameters is documented. It was found that increases in the obstacle thermal conductivity improve the internal obstacle heat flow through reduced temperature gradients with large values of the solid thermal conductivity (ksolid/kfluid ≥ 100) effectively isothermalizing the obstacles. Differences between two methods typically used to model the waste heat production in electronic devices, surface flux and volumetric heating, were found to only manifest themselves within the obstacle with only small changes in Nusselt numbers.