The Calculation of The Effective Thermal Conductivity of Media with Regularly Dispersed Parallel Cylinders

Abstract

In treating problems of thermal conduction in dispersive media, it is necessary to calculate the effective thermal conductivity instead of analyzing the detailed thermal field. The present paper aims to estimate the effective thermal conductivity of two-dimensional media with regularly dispersed materials by applying the boundary element method. Media with parallel cylinders dispersed at square lattice points are considered. It is assumed that two-dimensional thermal conduction takes place in the plane normal to these cylinders. In the case of regularly arranged circular cylinders, the present authors have also developed an exact analytical method. The present method is compared with the previous one by carrying out numerical calculation and the result is satisfactory. The method is also applied to analyze the case of cylinders of square cross section.