Ekaterina Pesetskaya

Improved algorithm for analytical solution of the heat conduction problem in doubly periodic 2D composite materials

We consider a boundary value problem (BVP) in unbounded 2D doubly periodic composite with circular inclusions having arbitrary constant conductivities. By introducing complex potentials, the BVP for the Laplace equation is transformed to a special -linear BVP for doubly periodic analytic functions. This problem is solved with use of the method of functional equations. The -linear BVP is transformed to a system of functional equations. A new improved algorithm for solution of the system is proposed. It allows one not only to compute the average property but to reconstruct the solution components (temperature and flux) at an arbitrary point of the composite. Several computational examples are discussed in details demonstrating high efficiency of the method. Indirect estimate of the algorithm accuracy has been also provided.

Analytical methods for heat conduction in composites

Abstract Analytical methods unifying the study of heat conduction in various type of composite materials are described. Analytical formulas for the effective (macroscopic) conductivity tensor are presented.

Calculations of the Thermal Conductivity of Porous Materials

In this paper, the geometrical effective thermal conductivity of porous materials is investigated based on two different approaches: the finite element method as a representative for numerical approximation methods and an analytical method for 2D homogenised models based on a solution of the respective boundary value problem. It is found that the relative conductivity is practically independent of the specific shape or topology of the inclusions. Only the morphology (closed-cell or open-cell) of the structure slightly influences the conductivity. Furthermore, it is shown that a small perturbation of the circular inclusions of 2D models increases the effective conductivity.

Solution to the Dirichlet problem for an infinite strip domain with holes

The aim of this work is to develop the method of functional equations to boundary value problems for a strip with mutually disjoint circular holes. The boundary of the strip domain, two parallel straight lines, is treated as two touching circles on the extended complex plane. The general algorithm is effectively implemented to computation of the local flux around holes.

Properties of a Composite Material with Mixed Imperfect Contact Conditions

We present an analytical solution of a mixed boundary value problem for an unbounded 2D doubly periodic domain which is a model of a composite material with mixed imperfect interface conditions. We find the effective conductivity of the composite material with mixed imperfect interface conditions, and also give numerical analysis of several of their properties such as temperature and flux.

Two different approaches for the effective conductivity investigation of 2D porous materials with temperature dependent material properties

The effective conductivity of 2D porous materials with temperature dependent matrix properties is investigated by two different approaches: namely, a numerical and an analytical method. A model with disjoint parallel cylindrical pores in a representative cell is considered. The numerical method is represented by the finite element method. In the scope of the analytical method, the nonlinear boundary value problem which describes conducting properties of the materials is solved by the methods of complex analysis, and the effective conductivity is represented in an explicit form via the solution of this problem. The values of the effective conductivity obtained by two these methods are compared.

The Effective Conductivity of 2D Porous Materials with Temperature Dependent Material Properties

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.