AbstractSome of the differential equations of thin fin theory have been rewritten to include an internal heat generation term, and solutions have been obtained for fins of rectangular, triangular, and“optimum”profiles. Fin temperature distributions and heat removal rates are exhibited as functions of the other variables involved by means of dimensionless parameters. In addition, criteria are discussed for determining whether the use of fins is worthwhile in a given application where internal heat generation is present in the fins.The analysis presented here should find wide application, not only to actual fins, but to many other problems where thin fin theory applies, such as determination of the heat transfer characteristics of thin structural members used in reactors.