This paper presents a three-dimensional geometric optimisation of conjugate cooling channels in forced convection with internal heat generation within the solid. Pentagonal cooling channels configuration are considered. The main objective is to optimise the configuration in such a way that the peak temperature is 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 elemental volume of the structure and hydraulic diameter of the cooling channel were considered 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 mathematic optimisation algorithm (Dynamic-Q) is applied in order to search for the best optimal geometric configuration that improves thermal performance by minimising thermal resistance for a wide range of dimensionless pressure difference. Results obtained show that there are unique optimal geometry for a given pressure difference. Also, the results show that the effects of dimensionless pressure drop on minimum thermal resistance and hydraulic diameter of the channel are consistent with those obtained in the open literature.
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