The radiative and convective heat transfer from a fin array consisting of longitudinal rectangular fins on a plane surface has been theoretically investigated by mathematically describing the interaction among the heat conduction in the fin, the convective heat transfer to the fluid medium, and the radiant exchange of the fin with the neighboring elements. Solutions for the fin temperature distribution, the local radiative heat fluxes over the fin and base surfaces, the total radiative heat transfer, the total convective heat transfer, and the effectiveness of the fins were found. In the primary range of physical interest, the fins usually cause a considerable increase in the convective component of the heat transfer but either cause decreases or only slight increases in the radiative component. Thus convection is generally the more effective mode of heat transfer in fin arrays, and the effectiveness of the fins decreases as the radiative component increases.