Optimization of a rectangular pin fin using rectangular perforations with different inclination angles

Perforated fins, because of their compactness, low weight and high effectiveness are widely used in heat sinks to enhance the heat transfer from electronic equipments. The innovative form of the perforated fin (with inclination angles) was considered for the rectangular pin fin. In the analytical solution, the Degenerate Hypergeometric Equation (DHE) was used as a new derivative method and then solved by Kummer’s series. Also, Signum function is used to model the opposite and mutable approach heat transfer area. This article presents a combined open literature and Experimental work of various cases to validate the analytical study. Two models were perforated experimentally at the 5mm from bottom tip at a various inclination angles by using a wire cut electrical discharge machining (Wire EDM) and EDM drilling machine. The present mathematical model has good reliability according to the high agreement of the validation results about (0.33%- 1.4%). It was found that use of the inclined perforation fin leads to decreased thermal resistance and improvement in the thermal performance of the pin fin by enhancing the heat transfer. Also, the optimization can be achieved by minimizing the weight and length of the pin fin based on the Multi advantages of the present model. Likewise, Entropy generation was minimized with increases the open area ratio at a certain Rayleigh number and constant heat flux.