This study discusses the development of the exact series solutions for the computation of temperature in parallel plate and circular porous passages. These passages are filled with relatively high thermal conductivity materials; and therefore, this study includes the contribution of axial conduction. This leads to the solutions for a set of modified Graetz type problems for parallel plate channels and circular pipes. The numerical procedure yields the Nusselt number that indicates significant variations depending on the size of the Peclet. The Nusselt number is computed for selected values of the Peclet number, mainly, to demonstrate the mathematical and numerical procedure. (c) 2005 Elsevier Ltd. All rights reserved.