Flow orientation in conjugate cooling channels with internal heat generation

Abstract

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.This work presents a three-dimensional geometric optimisation of conjugate cooling channels in forced convection with internal heat generation within the solid for an array of circular cooling channels with different flow orientations based on constructal theory. Three flow orientations were studied: Firstly, an array of channels with parallel flow; secondly, an array of channels in which flow of the every second row is in a counter direction to one another and thirdly, with the every flow in the array of channels in counter direction to one another. The geometric configurations and the flow orientations were optimised in such a way that the peak temperature was minimised subject to the constraint of fixed global volume of solid material. The cooling fluid was driven through the channels by the pressure difference across the channel. The system had hydraulic diameter and channel to channel spacing as degrees of freedom of the design variables. A gradient-based optimisation algorithm was applied to search for the best optimal geometric configurations that improve thermal performance by minimising thermal resistance for a wide range of dimensionless pressure differences. This optimiser adequately handles the numerical objective function obtained from numerical simulations. The effect of porosities, applied pressure difference, flow orientation and heat generation rate on the optimal hydraulic diameter and channel to channel spacing were reported. Results obtained show that the effects of dimensionless pressure drop on minimum thermal resistance were consistent with those obtained in the open literature.