Optimisation of conjugate triangular 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 a conjugate cooling channel in forced convection with an internal heat generation within the solid for isosceles right triangular channel and equilateral triangular channel configurations. The isosceles right triangle and equilateral triangle are special case of triangle which can easily and uniformly be packed and arranged to form a larger constructs. The configurations 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 is driven through the channels by the pressure difference across the channel. The structure has channel height, width and channel to channel spacing as degrees of freedom as design variables. The shape of the channel is allowed to morph to determine the best configuration that gives the lowest thermal resistance. A gradient-based optimisation algorithm is applied in order to search for the best optimal geometric configurations that improve thermal performance by minimising thermal resistance for a wide range of dimensionless pressure difference. This optimiser adequately handles the numerical objective function obtained from CFD simulations. The effect of porosities, applied pressure difference and heat generation rate on the optimal aspect ratio and channel to channel spacing are reported. There are unique optimal design variables for a given pressure difference The numerical results obtained are in agreement with the theoretical formulation using scale analysis and method of intersection of asymptotes Results obtained show that the effects of dimensionless pressure drop on minimum thermal resistance are consistent with those obtained in the open literature.