A Ubiquitiformal One-Dimensional Steady-State Conduction Model for a Cellular Material Rod

Abstract

A ubiquitiformal model for the one-dimensional steady-state heat transfer of a cellular material rod is developed in this paper, and the explicit analytical expressions for both the temperature distribution and the equivalent thermal conductivity are obtained. The calculated results for two kinds of dry soil are found to be in good agreement with previous experimental data. Moreover, it is demonstrated that the ubiquitiformal model is more reasonable for describing such a cellular material than the fractal one, and hence a ubiquitiformal rather than a fractal model should be considered in practical applications whenever the integral dimensional measure of a real physical object must be taken into account.