Bounding of effective thermal conductivity of two-phase materials

摘要

In this paper, we propose a new approach to obtain the upper and lower bounds for the effective thermal conductivity of real two-phase systems. The developed expressions are based upon the series and parallel combination of resistors. To incorporate the effect of random distribution of inclusions in the continuous matrix as well as the wide difference in the thermal conductivity of the constituents, a non-linear second-order correction term is introduced. This correction term is used to replace the volume fraction of inclusions in parallel and perpenducular thermal conductivity equations. The obtained upper and lower bounds are then compared with the Hashin and Shtrikman bounds [1] and it is found that the modified bounds are narrower as compared to other previously developed bounds for effective thermal conductivity. The modified upper and lower bounds are then used in Chaudhary and Bhandari's model to predict the effective thermal conductivity of real two-phase materials. The predictions of the effective thermal conductivity using the modified relations match well with the experimental results.