Abstract The almost two-dimensional steady-state rates of heat loss from arrays of uniformly-spaced vertical rectangular fins, extending upwards—in otherwise stagnant air—from horizontal heated bases, have been measured. (The vertical air gaps between the fins were closed at their sides, by insulated vertical end-barriers.) The effects of various combinations of height, thickness and spacing of the fins, for different base temperatures (in the range 40 to 100°C), have been studied. For the configuration considered, in a normal ambient environment (∼ 20°C), there is an optimal fin spacing (⋍ 16 mm) corresponding to the greatest steady-state rate of free convective/conductive heat loss through the air from the finned system, and this is almost independent of the temperature of the heat exchanger base (in the range 40–100°C). At this optimal spacing for base temperatures not greater than 50°C, the convective/conductive heat transfer rate from the array increases with the fin height up to about 60 mm, so that it would be uneconomic to employ taller fins if convection/conduction is dominant compared with radiation. If the radiation contribution is also considered, then the optimal spacing corresponding to the maximum total steady-state rate of heat loss through the air is somewhat less than the optimal spacing for which, under the same temperature conditions, the maximum steady-state rate of convective/conductive heat leak occurs. The greater the emissivity of the heat exchanger surfaces, the narrower the optimal uniform gaps between the fins. A two-dimensional finite-difference computer program has been composed to predict the temperature distribution throughout the heat exchanger for a stipulated ambient environmental temperature and experimentally-determined distribution of the heat transfer coefficient over the surfaces of the exchanger. This enables, for instance, any hot spots to be located prior to a proposed design being built.