Thermal management of parabolic pin fin subjected to a uniform oncoming airflow: optimum fin dimensions

Abstract

A concave-parabolic pin fin (spine) is considered within the present research. The thermal property of the spine is exhibited to be affected by a uniform oncoming airflow in an aim at improving its cooling performance. The mathematical model corresponding to one-dimensional physical layout is formulated first from the usual heat balance method. Exact and numerical solutions of the fin temperature distribution are then extracted from the model, relying upon two physical parameters: namely, the Peclet number Pe, controlling the magnitude of the airflow and the fin shape parameter $$\alpha$$ , adjusting the spine shape. It is shown that these parameters have high impacts on the performance of the parabolic pin fin towards cooling the medium it is attached to. Finally, optimum concave parabolic pin fins corresponding to a given volumetric region are identified by means of maximizing the base heat transfer rate. Interestingly, the optimum dimensions of the spine are found to be much influenced by the variation in Peclet number.