LAUSR

An innovative form of a perforated fin (with inclination angles) was considered. In most previous studies, pin fins were perforated in a straight direction to improve the thermal performance of the heat sink. The present rectangular pin fin consisted of an elliptical perforation with two models and two cases. The signum function was used to model the opposite and mutable approach of the heat-transfer area. The degenerate hypergeometric equation was used as a new derivative method to determine a general solution and solved by Kummer’s series. Two validation methods (previous work and Ansys 16.0 steady-state thermal analysis) were considered. The strong agreement of the validation results (0.31 %-0.52 %) showed the reliability of the presented model. The use of the perforated fin reduced the thermal resistance and improved the thermal performance of the pin fin by enhancing heat transfer and increasing the Nusselt number. Moreover, increasing the inclination angle, size, and number of perforations can optimize the present model by maximizing heat transfer and minimizing the weight and length of the pin fins. Increasing the open-area ratio minimizes entropy generation at a certain Rayleigh number and constant heat flux.