Thermal–Hydraulic Optimization of Slotted Pin Fins Under Laminar Flow Using Response Surface Methodology

Abstract

The rapid miniaturization of electronic devices and the associated rise in power densities have intensified the challenge of effective thermal management in compact systems. Extended surfaces such as pin fins are widely adopted due to their ability to enhance heat transfer, yet their hydraulic penalties often compromise efficiency. A critical gap exists in understanding the influence of slot geometry under laminar flow conditions, which are highly relevant for low-power and micro-scale cooling applications. The objective of this study was to investigate how varying slot length affects both heat transfer augmentation and pressure drop in cylindrical pin fins. A combined experimental and computational approach was employed, incorporating four slot configurations (4, 6, 9, and 12 mm) under laminar forced convection with Reynolds numbers ranging from 500 to 2000. Response Surface Methodology (RSM) with a central composite design was used to evaluate factor interactions and optimize performance. Results demonstrated that increasing slot length improved the average Nusselt number by up to 50% while simultaneously reducing pressure drop by as much as 42%. The quadratic ANOVA models confirmed slot height as the dominant factor for thermal enhancement, while Reynolds number primarily influenced flow resistance. Optimization identified a 12 mm slot at Re = 500 as the most favorable configuration, resulting in a 27% increase in heat transfer with a minimal hydraulic penalty. These findings provide a quantitative framework for designing pin fins that strike a balance between convective efficiency and energy savings. Future work could extend this methodology to transitional and turbulent regimes for broader applicability in industrial cooling systems