Response to Comments in Exact and -exact- formulae in the theory of composites (arXiv:1708.02137v1 [math-ph], 7 August 2017)

TL;DR

This paper addresses comments on a previous study about calculating the effective thermal conductivity of complex multiscale ordered arrays, clarifying the methodology and findings.

Contribution

It provides a detailed response to critiques, clarifying the theoretical approach used in determining effective thermal properties of composite materials.

Findings

Clarification of the theoretical framework

Rebuttal of previous critiques

Strengthening of the original methodology

Abstract

In this paper we present our response to the comments by Andrianov and Mityushev regarding a recent publication of ours on the determination of the effective thermal conductivity of multiscale ordered arrays.