Constructal entropy generation rate minimization for asymmetric vascular networks in a disc-shaped body

Abstract

Based on constructal theory, the vascular networks with asymmetric pairing in a disc-shaped body are optimized by taking the minimizations of the dimensionless entropy generation rate and dimensionless entropy generation ratio as optimization objectives, respectively. The results show that there exist optimal tube lengths and angles which lead to the minimum dimensionless entropy generation rate and dimensionless entropy generation ratio of the vascular networks with two and three levels of asymmetric pairing, respectively. The optimal constructs of the vascular networks based on asymmetric and symmetric designs are different. For the specified heat flow per unit length on each tube surface, when the number of outlets N=24 and the dimensionless mass flow rate M1∗=10-2, the dimensionless entropy generation rate with two levels of pairing based on asymmetric design is decreased by 7.80% than that based on symmetric design; when the number of outlets N=24 and the dimensionless pumping power W̃2∗=1, the dimensionless entropy generation rate with three levels of pairing based on asymmetric design is decreased by 6.78% than that based on symmetric design. Moreover, the performance improvements of the vascular networks with asymmetric design can also be found for the specified heat flux on each tube surface. The optimization results of the vascular networks based on minimum flow resistance are special cases of those based on minimum entropy generation rate in this paper.