As a preliminary study of the nature of heat transfer between a packed bed and a bounding wall, a first-order model is considered where the bed is taken to be a row of rectangular compacts. Results are obtained numerically for the fluid flow and heat transfer in the voids between compacts and to the wall. Different gap sizes and compact-plane separations, with Prandtl numbers of 0.72 and 7 and Reynolds numbers ranging from 0 to 100, are considered. As the compact separation and the Reynolds number increase, the heat transfer from the void increases and the maximum temperature decreases. Increasing the Prandtl number improves the heat transfer from the void, and when the compact-bounding plane separation increases, the fluid flow and heat transfer settle down to essentially a stationary value, independent of the Reynolds number.