The effective conductivity of 2D porous materials with temperature dependent material properties

Abstract

The effective conductivity of 2D doubly periodic porous materials with temperature dependent material properties is investigated. An arbitrary number of disjoint parallel cylindri- cal pores in a representative cell is considered. A multiply connected unbounded domain in the complex plane can serve as a geometrical description of such kind of materials. The problem of determination of the effective conductivity can be reduced to a boundary value problem for the Laplace equation on the multiply connected domain. This problem is analytically solved by the method of functional equations. An explicit formula for the effective conductivity is found. It contains the basic models’ parameters and elliptic Eisenstein functions.