This study addresses the electronic cooling problem from the perspective of scaling laws applied to a simple conjugate heat transfer geometry, steady shear flow over a heated strip on a flat plate. The results are reported in a compact form in terms of a modified Nusselt number and a combined parameter (k f /k s )Pe 1 3 . Numerical results are reported that apply to a wide range of values for fluid flow, thermal conductivity, and thickness of the flat plate, and the results include simple design correlations. A new dimensionless parameter is suggested for determining when the fluid axial heat conduction can be neglected.