The flow in the region between two infinite rows of rectangular compacts lying between two planes is considered in an attempt to model the heat transfer and fluid flow near the bounding wall of a packed bed. In this region it is known that the voids are larger than those in the center of the bed, giving rise to an enhanced flow near the wall. The equations governing the fluid flow and heat transfer are solved numerically for a range of compact-plane separations and compact-compact separations, with Prandtl numbers of 0.72 and 7.0 and Reynolds numbers ranging from 0 to 50. It was found that as the Reynolds number increased, the heat transfer from the void decreased, although increasing the void size led to some improvement in the heat transfer from the void. Also, the heat transfer from the void increased when the Prandtl number decreased, but when the compact-plane separation was increased the heat transfer in the void was greatly reduced with the temperature of the fluid becoming nearly uniform.