A numerical investigation was conducted on the heat, transfer from a uniformly powered strip source of heat located on the surface of a two-dimensional conducting substrate. The upper and lower surfaces of the substrate are cooled by forced laminar flow that is two-dimensional, steady and with constant properties. The problem is a paradigm for the investigation of the competing effects of substrate conduction and fluid convection in the cooling of electronic components, i.e., chips or chip carriers, on boards or substrates that are cooled by air flowing parallel to the surface. The objectives of the study were to investigate the conjugate heat transfer mechanisms in great detail and in a methodical way, such as to use the results as a baseline for successively more complex situations of air-cooling of on-board components. Results are presented for the substrate conductivity to fluid conductivity ratio, k(s)/k(f) from 0.1 to 100, channel Reynolds number from order 100 to order 1000, corresponding to air velocities of order 1 m s(-1) and for both developing and fully developed laminar, parallel-plane channel flow.