The study of heat transfer in rectangular passages with prescribed wall heat flux is of practical interest. These passages could be open or filled with saturated porous materials. A solution that uses the Green's function can accommodate the inclusion of heat flux over the entire surface area or over isolated sections of the boundary. Also, this solution permits the inclusion of frictional heating. Two different boundary conditions are considered: constant wall temperature and constant wall heat flux. The computed heat transfer coefficients show that the thermally fully developed condition may not be attainable in practical applications for very narrow passages with prescribed wall heat flux. (c) 2006 Elsevier Ltd. All rights reserved.