A comparative study of longitudinal fins of rectangular, trapezoidal and concave parabolic profiles with multiple nonlinearities

This paper establishes the performance characteristics of convective–radiative longitudinal fins of rectangular, trapezoidal and concave parabolic profiles with simultaneous variation of thermal conductivity, heat transfer coefficient and surface emissivity with temperature. The convection and radiation sink temperatures were assumed to be non-zero. The calculations are carried out using the differential transformation method (DTM). The accuracy of the DTM is confirmed by comparing its predictions with the results from an analytical solution and a well-tested numerical procedure. A new idea of volume adjusted fin heat transfer rate, fin effectiveness, and fin efficiency is introduced to compare the performances of trapezoidal and concave parabolic fins with the rectangular fin. Results presented illustrate the effects of thermal conductivity parameter, emissivity parameter, convection–conduction parameter, radiation–conduction parameter, and dimensionless convection and radiation sink temperatures on the performance of fins.