AN ANALYTICAL MODEL FOR EFFECTIVE THERMAL CONDUCTIVITY OF THE MEDIA EMBEDDED WITH FRACTURE NETWORKS OF POWER LAW LENGTH DISTRIBUTIONS

Abstract

The effective thermal conductivity of porous media is of steady interest in the design of new materials. In this study, an analytical model for dimensionless effective thermal conductivity of media embedded with fracture networks of the power law length distributions is proposed. It is found that the proposed dimensionless effective thermal conductivity is a function of micro-structural parameters of media, such as the porosity [Formula: see text] and fracture orientation (dip [Formula: see text] and azimuth [Formula: see text]). The present results show that the dimensionless effective thermal conductivity of the media increases with the increase in the ratio [Formula: see text] and the power law exponent [Formula: see text] at [Formula: see text]. Inversely, when [Formula: see text], it decreases with the increase in the power law exponent [Formula: see text]. In addition, the dimensionless effective thermal conductivity is gradually independent of the orientation as the ratio [Formula: see text]. The present model may provide a significant insight into the mechanism of heat transfer in the media embedded with fracture networks of power law length distributions.