A simple one-dimensional vertically averaged model for heat transfer through a conductive partition separating two reservoirs at different temperatures has been developed. The model essentially assumes a linear increase of temperatures in the vertical direction, both in the two reservoirs and in the partition. Therefore, the heat flux across the partition is independent of height, and becomes constant. In this article we consider the cases, where at least one of the reservoirs is filled with a fluid-saturated porous medium. In the porous reservoir the Darcy's law and thermal equilibrium between fluid and porous matrix are assumed. According to the proposed model a unique non-dimensional parameter a is identified as a single parameter to govern the convection-conduction conjugate problem. The parameter a physically means a ratio of thermal resistance between the partition and the respective reservoirs. The a is found to be the same parameter proposed by Bejan in an earlier study, except for a numerical factor. The present analysis is compared with Bejan's results for special cases dealing with the average heat transfer rate and the average partition temperature. It is found that the present model well predicts Bejan's results. The one-dimensional model on porous-fluid system is also tested with experiments, and the model predictions generally agree well with the experimental ones. Copyright (C) 2003 John Wiley Sons, Ltd.