Constructal flow orientation in conjugate cooling channels with internal heat generation

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 array of circular cooling channels with different flow orientation. Three flow orientations were studied: array of channels with parallel flow; array of channels in which the flow in every second row is in a counter direction with its neighbours, and flows in all the arrays of channels are in counter flow relative to each other. The geometric configurations were determined in such a way that the peak temperature was minimised subject to the constraint of fixed global volume of solid material. The degrees of freedom of the design were hydraulic diameter and channel to channel spacing. 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. The effect of porosities, applied pressure difference, flow orientation and heat generation rate on the optimal hydraulic diameter and channel to channel spacing is reported. The results show that the effects of dimensionless pressure drop on minimum thermal resistance were consistent with those obtained in the open literature.