Numerical optimisation of square pin-fins for minimum thermal resistance with non-uniform design dimensions

Abstract

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.

In this paper we apply constructal theory and design to present a three-dimensional geometric optimisation of cooling square pin-fins in forced convection of solid base material subject to constant temperature at the bottom. The main objective was to optimise the configuration in such a way that the peak temperature was minimised from the solid to the fluid of the pin fin. The cross–sectional area of solid base was fixed and the thickness of the solid is allowed to change. Three design cases are considered; the Case 1 has the pin-fins in a single row, Case 2 configuration has the pin-fins in two rows and Case 3 has configuration of the pin-fins in three rows arrangement. In all the three cases, the pin-fins geometric dimension are not uniform. The structure had four degrees of freedom as design variables: thickness of the solid base, hydraulic diameter of the pin, the height of the pin and pin spacing. The shape of the pin was not fixed but allowed to morph 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 stream velocity. An optimisation algorithm called Dynamic-Q was applied in order to search for the best optimal geometric configuration 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.