The boundary element method (BEM) has been used to investigate the two-dimensional temperature distribution and the flow of heat from a polygonal fin with two tubes on a square pitch. This numerical method is shown to be convergent, stable and consistent. The resultant heat flows from the fin and the tubes are presented in the form of fin performance ratios. The values of the two-dimensional fin performance ratios are almost identical to those obtained for a single radial rectangular fin of equivalent surface area. The one-dimensional fin performance indicators, fin performance ratio or fin efficiency can be used to predict the heat flows. However, the two-dimensional temperature distributions have revealed the existence of conductive paths between the two tubes depending upon the fin dimensions, the values of the heat transfer and material thermal conductivity, and the magnitude of the temperature differences between the two tubes and the surrounding air. (c) 2005 Elsevier Ltd. All rights reserved.