Heat transfer to a fluid passing through a channel filled with porous materials is the subject of this investigation. It includes the derivation of the temperature solutions in channels having different cross sectional geometries. Primarily, consideration is given to a modified Gractz problem in parallel plate channels and circular tubes. This presentation includes numerical features of the exact series solution for these two ducts using the Brinkman's model. The results are compared to results from another numerical study based on the method of weighted residuals. Moreover, as a test case, the method of weighted residuals provided flow and heat transfer in elliptical passages. The results include the computation of heat transfer to fluid flowing through elliptical passages with different aspect ratios. (C) 2003 Elsevier Ltd. All rights reserved.