Derivation of the unifying model and its discussion on the effective thermal conductivity of isotropic, porous and composite media

Abstract

A detailed and primordial derivative process of the classical Maxwell problem applied to thermal conductivity was presented in this study, aiming to offer a foundation for further research on various correlations predicting the effective thermal conductivity (ETC) of porous-composite media, especially for the unifying equation with five fundamental structural models. This process of theoretical analysis is, in essence, solving the Laplace's Equation for temperature distribution in a spherical coordinate under certain initial and boundary as well as other assumed conditions. The particular solution processes also overcome various degrees of shortcomings existed in previous literatures in this field, e.g. problems of nondegenerate, insufficient boundary conditions and many tiny mistakes (typos or misprints). We hope this commentary letter can maintain the rigor of academic research in a rightful and suitable form, and prevent any potential confusion for future readers in this field.