Embedded converging surface microchannels are developed as effective new ways of reducing entropy production in boundary layer flow with convective heat transfer. A similarity solution with slip-flow boundary conditions is developed to find the spatial distributions of velocity, temperature, wall shear stress and wall heat flux. Mixed Knudsen number conditions along the surface require both slip-flow and no-slip formulations to be combined in an integral solution. Predicted results from the method of EBSM (entropy based surface micro-profiling) are presented for the optimized microchannel aspect ratio, spacing between adjacent microchannels and the angles characterizing the converging microchannels. (C) 2004 Elsevier Ltd. All rights reserved.