Variabilities and their upper and lower bounds of the equivalent thermal conductivity and resistance defined by the entransy dissipation rate

The prediction of equivalent thermal conductivity (ETC) and resistance (ETR) is an important topic in the composite material field. Many expressions of ETCs and ETRs have been proposed using different homogenization methods in last several decades. Especially, expressions defined by the entransy dissipation rate, k(eff) and R-eff, excel for their wide range of application. Usually, it was agreed that k(eff) and R-eff were determined by the thermal conductivity distribution inside. However, we find that they are also vary with the boundary temperature gradient distribution (TGD). In this paper, we simulate and mathematically prove the influence of boundary TGD on k(eff). The results indicate that k(eff) with uniform boundary TGD is higher than that with non-uniform boundary TGD. In addition, the mathematical proof after a little adjustment is applied to confirm the minimum thermal resistance principle based on the uniform TGD inside. The results show that k(eff) is the maximum when TGD are uniform in all regions including boundaries, and k(eff) reaches the minimum when the non-uniformity of TGD extends to the limit. Upper and lower bounds of k(eff) and R-eff found in this paper are greatly valuable for optimizing the heat transfer ability and heat insulation ability of materials. And the methodology as well as conclusion in this paper can be reproduced in some generalized irreversible transport systems. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

The prediction of equivalent thermal conductivity and resistance in composite materials is crucial, and this study reveals the impact of boundary temperature gradient distribution on these parameters. It is found that when the boundary temperature gradient is uniform, the equivalent thermal conductivity is higher, whereas a non-uniform distribution results in lower equivalent thermal conductivity. Mathematical proof confirms the minimum thermal resistance principle based on uniform temperature gradient distribution inside.