This paper presents the development of the three-dimensional flow architecture of conjugate cooling channels in forced convection with internal heat generation within the solid for an elliptical cooling channel configuration. The main objective was to optimise the configuration in such a way that the peak temperature was minimised subject to the constraint of the fixed global volume of solid material. The cooling fluid was driven through the channels by the pressure difference across the channel.

The structure had three degrees of freedom as design variables: elemental volume, channel hydraulic diameter and channel-to-channel spacing. The shape of the channel is allowed to morph to determine the best configuration that gave the lowest thermal resistance. A gradient-based optimisation algorithm was applied in order to search for the best optimal geometric configuration that improved thermal performance by minimising thermal resistance for a wide range of dimensionless pressure difference. The effect of porosities, applied pressure differences and heat generation rate on the optimal geometry was reported. There are unique optimal design variables for a given pressure difference. Results obtained show that the effects of dimensionless pressure drop on minimum thermal resistance were consistent with those obtained in the open literature.

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