Analysis is presented for conjugate heat transfer in a parallel-plate microchannel. Axial conduction in the fluid and in the adjacent wall are included. The fluid is a constant property liquid with a fully-developed velocity distribution. The microchannel is heated by a uniform heat flux applied to the outside of the channel wall. The analytic solution is given in the form of integrals by the method of Green's functions. Quadrature is used to obtain numerical results for the local and average Nusselt number for various flow velocities, heating lengths, wall thicknesses, and wall conductivities. These results have application in the optimal design of small-scale heat transfer devices in areas such as biomedical devices, electronic cooling, and advanced fuel cells. (c) 2011 Elsevier Ltd. All rights reserved.