Constructal entransy dissipation rate minimization for leaf-like fins

Abstract

Based on constructal theory, the constructs of the leaf-like fins are optimized by taking minimum entransy dissipation rate (for the fixed total thermal current, i.e., the equivalent thermal resistance) as optimization objective. The optimal constructs of the leaf-like fins with minimum dimensionless equivalent thermal resistance are obtained. The results show that there exists an optimal elemental leaf-like fin number, which leads to an optimal global heat conduction performance of the first order leaf-like fin. The Biot number has little effects on the optimal elemental fin number, optimal ratios of length and width of the elemental and first order leaf-like fins; with the increase of the thermal conductivity ratio of the vein and blade, the optimal elemental fin number and optimal ratio of the length and width of the elemental leaf-like fin increase, and the optimal shape of the first order leaf-like fin becomes tubbier. The optimal construct based on entransy dissipation rate minimization is obviously different from that based on maximum temperature difference minimization. The dimensionless equivalent thermal resistance based on entransy dissipation rate minimization is reduced by 11.54% compared to that based on maximum temperature difference minimization, and the global heat conduction performance of the leaf-like fin is effectively improved. For the same volumes of the elemental and first order leaf-like fins, the minimum dimensionless equivalent thermal resistance of the first order of the leaf-like fin is reduced by 30.10% compared to that of the elemental leaf-like fin, and the global heat conduction performance of the first order leaf-like fin is obviously better than that of the elemental leaf-like fin. Essentially, this is because the temperature gradient field of the first order leaf-like fin based on entransy dissipation rate minimization is more homogenous than that of the elemental leaf-like fin. The dimensionless equivalent thermal resistance defined based on entransy dissipation rate reflects the average heat transfer performance of the leaf-like fin, and can provide some guidelines for the thermal design of the fins from the viewpoint of heat transfer optimization.