Analytical solution for evaluating the thermal performance and efficiency of convective–radiative straight fins with various profiles and considering all non-linearities

Abstract If the temperature change from the base to the tip of the fin is large, then for an accurate prediction of the performance of the fin, the model must incorporate the variation of thermal conductivity with temperature. Also, the heat exchange with the surrounding air is associated with the heat transfer coefficient. It has been experimentally proven that the heat transfer coefficient may not be uniform and there are large differences in the heat transfer coefficient both from fin base to fin tip and along the fin in the direction of the airflow. Same as two parameters mentioned above, the surface emissivity and internal heat generation within the fins may vary with temperature. This paper analytically investigates the temperature distribution within convective–radiative straight fins with simultaneous variation of thermal conductivity, heat transfer coefficient, surface emissivity and internal heat generation with temperature. Also, convection and radiation sink temperatures were assumed to be non-zero. Four different longitudinal fins such as rectangular, triangular, convex and exponential were considered. The calculations are carried out using the well-known approximate analytical differential transformation technique. Fin efficiency and the effects of some physically applicable parameters in this problem such as thermal conductivity, convection–conduction parameter, radiation–conduction parameter, convection sink temperature and radiation sink temperature were studied comparatively. Because a broad range of governing parameters are investigated, the results should be useful in a number of engineering applications.