Abstract Steady-state free and forced convective cooling of vertical, rectangular, 3 mm thick, 250 mm long fins, uniformly separated and protruding vertically upwards from a 250 mm × 190 mm isothermal horizontal base was investigated. For each combination of specified fin protrusion, horizontal forced air flow-rate in the direction along the fins and fin base temperature, the optimal fin spacing—corresponding to the maximum rate of heat loss—has been deduced. As the fin protrusion of the heat exchanger increases, this optimal value rises significantly in forced convection conditions, but declines slightly in the presence of free convection alone. The temperature distributions over the fins' surfaces were also studied, when the fin base was maintained at constant temperatures of either 40°C, 60°C or 80°C above that of the ambient environment. Large temperature depressions occurred near the leading edges and tips of the fins in forced convection, whereas much nearer isothermal temperature distributions were present under free convection conditions.