Constructal entransy dissipation rate minimization for “disc-to-point” heat conduction

Abstract

Based on constructal theory, “disc-to-point” heat conduction is optimized by minimizing the entransy dissipation rate whereby a critical point is determined that distributes the high-conductivity material according to optimized radial or branch patterns. The results show that the critical point is determined by the product of the thermal conductivity ratio of the two materials and the volume fraction of the high-conductivity material allocated to the entire volume. The notion of optimal heat transfer performance can be attributed to the disc based on the entransy dissipation extremum principle. Comparing the results based on EDR minimization (entransy dissipation rate minimization) with those based on MTD minimization (maximum temperature difference minimization), one finds that the performance derived from the two optimization procedures are different. When the product of the thermal conductivity ratio and volume fraction is 30, the critical point of the former procedure is that for which the nondimensional radius of the disc equals 1.75, while that of the latter procedure is that for which this radius of the disc equals 2.18. Comparing heat transfer performances from the two procedures, the mean heat transfer temperature difference is decreased more for the former procedure thereby receiving an improved performance quota.