Constructal optimization for “disc-point” vascular networks based on minimum entransy dissipation rate

Abstract

For the specified total area of the disc and total volume of the vascular network, the constructal optimizations of the first order, second order and third order vascular networks are carried out by taking the minimizations of the entransy dissipation rate and entransy dissipation number, caused by heat transfer with finite temperature difference and flow resistance, as optimization objectives. The optimal constructs for each order vascular network with minimum entransy dissipation rate and entransy dissipation number are obtained. The results show that when the parameter B 1≥10-4, for the same dimensionless mass flow rate M *(1≤ M *≤102), the optimal constructs of the first order vascular network based on the minimizations of entransy dissipation rate and entropy generation rate are obviously different. For the second order vascular network, when the dimensionless mass flow rate locates at the range of 1≤ M *≤102, the magnitude orders of the entransy dissipations caused by heat transfer and flow resistance locate at the same level, and the optimal construct of the vascular network varies obviously with the change of the mass flow rate. For the same total volume of the vascular network and radius of the disc, when the dimensionless mass flow rates of the vascular networks are equal, the first order, second order and third order vascular networks almost exhibit the same performances of the entransy dissipation number; when the dimensionless pumping power satisfies , the minimum entransy dissipation number of the vascular network decreases with the increase in the order of the vascular network, and the performance of the vascular network can be improved by increasing the complexity of the vascular network in this case. Moreover, the performance of the vascular network is also optimized by taking complex index of entransy dissipation rate as optimization objective in this paper. The optimal results obtained in this paper can provide some guidelines for the designs of the vasculature from the point of view of heat transfer optimization.