UKHTC2013/54 54-1 13 th UK Heat Transfer Conference, UKHTC2013 2 - 3 September 2013 Imperial College London Optimisation of Multiple-Arrays of Cylindrical Pin- Fins for Minimum Thermal Resistance Olabode T. OLAKOYEJO 1 , Surajudeen O. OBAYOPO 2 , Lauber MARTINS 3 , Josua. P. MEYER 3 1 Department of Mechanical Engineering, University of Lagos, Lagos, Nigeria. 2 Department of Mechanical Engineering, Obafemi Awolowo University, Ife-Ife, Nigeria. 3 Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, South Africa. Abstract This paper presents a three-dimensional geometric optimisation of cooling cylindrical pin-fins in forced convection of a solid base material subjected to heat at a constant wall temperature applied at the bottom of the pin-fin heat sink. The main objective was to optimise the configuration in such a way that the thermal resistance was minimised. The cross-sectional area of solid base was fixed and the thickness of the base was allowed to change. The structure had four degrees of freedom as design variables, namely: thickness of the solid base, hydraulic diameter of the pin, height of the pin and pin spacing. The geometry of the pins was not fixed but allowed to morph in order to determine the best configuration, which gave the lowest thermal resistance. The cooling fluid (air) was driven by forced convection to the pin-fin by the constant velocity that corresponded to Reynolds number. An optimisation algorithm was applied in order to search for the best optimal geometry of pin-fins which improved thermal performance by minimising thermal resistance for a wide range of Reynolds number. The effect of applied Reynolds number and constant wall temperature on the optimal geometry was reported. There was unique optimal design geometry for a given Reynolds number. Results obtained show that the effects of Reynolds number on minimised thermal resistance are consistent with those obtained in the open literature. Keywords: Pin-fin, Optimisation, Laminar flow, Forced convection, Constructal theory, Thermal resistance. 1 Introduction Cylindrical pin-fin heat sinks are commonly used in industries in the cooling systems of electronic components. The design of heat sinks has become critical to the global performance of electronic packages as heat flux densities increase with the miniaturisation of the product. The heat sinks must be designed and maintained without exceeding a satisfactory and allowable work temperature specified by the manufacturers [1]. Bejan and Morega [2] studied the geometry of an array of fins that minimise the thermal resistance between the substrate and the forced flow through the fins by modelling the array as the Darcy-flow porous medium and the local thermal conductance in dimensionless form. Peles et al. [3] conducted the convective heat transfer and fluid flow analysis across a pin-fin micro heat sink. They concluded that the cylindrical micro-pin-fin heat sink solution is superior to that of a microchannel heat sink. Bejan [4] studied and extended the work of Jubran et al. [5] by providing the existence of an optimal spacing between the cylinders. Khan et al. [6] studied the optimal geometry of pin-fin heat sinks by an entropy generation minimisation for both in-line and staggered configurations. It was shown that In-