Abstract

The comment by Nunes suggests a welcome refinement to an approximation made in the original paper. We show here that Nunes’ refinement is identical to a modified effective thermal conductivity, keff ¼ k(1 + gZT), where k is the thermal conductivity, ZT is the usual material figure of merit, and g is in the range 0.4–0.5. This form of keff was already identified in Section 3.3 of our original paper as an option to improve the accuracy of the calculations and is itself an approximation to the more sophisticated keff analysis of Baranowski, Snyder, and Toberer [J. Appl. Phys. 113, 204904 (2013)]. As noted by Nunes and ourselves, the main downside of such refinements is that they complicate the universality of the main result, the universal cost surface in Fig. 2 of the original paper. The simplified results in the original manuscript are justified and reasonable for ZT ~1 or less, for physical insight, scaling, and rapid screening. For the best accuracy in real systems, exact numerical solutions of the coupled cost and power equations are most appropriate, examples of which we have recently published for 30 bulk and thin film materials in Renewable Sustainable Energy Rev., 32, 31.