An iterative method for the solution of the conjugate heat transfer problem is presented. Convection heat transfer in a channel is solved using an FDM, and conduction heat transfer in the channel wall is solved using a BEM. The FDM and BEM are coupled to iteratively solve the conjugate problem. Numerical results are in good agreement with experimental data. The influences of the conductivity ratio of solid on fluid, solid wall thickness, channel aspect ratio, and of the input velocity on the interfacial temperature and Nusselt number distribution are studied.