Experiments were performed to determine heat transfer coefficients on an upstream-facing surface that is pierced by a regular array of holes. The holes were arranged on equilateral triangular centers, and this regular geometry gives rise to a symmetry pattern whereby each hole is surrounded by a hexagonal region, the boundaries of which are symmetry lines. Within each such hexagonal module, the heat transfer and fluid flow characteristics are identical to those of all the other modules which blanket the surface, so that measurements for a single module yield information for the entire surface. This feature has been employed in the design and execution of the present experiments. Two parameters were varied during the course of the experiments-the hole pitch-to-diameter ratio P D and the per-hole Reynolds number Re. The results were tightly correlated by the relation NuL * = 0.881 Re0.476 Pr 1 3. The characteristic dimension in the Nusselt number is the ratio of the module surface area to the pitch, while the Reynolds number is that for flow through a pipe having a diameter equal to that of the holes in the plate. Flow visualization studies confirmed the existence of the array of hexagonal modules.