Application of MFS for determination of effective thermal conductivity of unidirectional composites with linearly temperature dependent conductivity of constituents

In this paper the problem of the effective conductivity in composite material is considered. It is assumed that the thermal conductivity coefficients of both the matrix and fibres materials are temperature-dependent. It yields the temperature-dependency of the effective thermal conductivity. To dete...

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Bibliographic Details
Published in:Engineering analysis with boundary elements 2012-03, Vol.36 (3), p.293-302
Main Authors: KOLODZIEJ, Jan A, USCILOWSKA, Anita
Format: Article
Language:English
Subjects:
Boundary value problems
Classical transport
Composite material
Effective thermal conductivity
Exact sciences and technology
Fibers
Fibres
Fundamental areas of phenomenology (including applications)
Heat conduction
Heat transfer
Mathematical analysis
Mathematical models
Mathematics
Method of fundamental solutions
Methods of scientific computing (including symbolic computation, algebraic computation)
Nonlinearity
Numerical analysis. Scientific computation
Partial differential equations
Physics
Sciences and techniques of general use
Statistical physics, thermodynamics, and nonlinear dynamical systems
Temperature dependent thermal conductivity
Thermal conductivity
Transport processes
Trefftz method
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Summary:In this paper the problem of the effective conductivity in composite material is considered. It is assumed that the thermal conductivity coefficients of both the matrix and fibres materials are temperature-dependent. It yields the temperature-dependency of the effective thermal conductivity. To determine the effective thermal conductivity a unit-cell approach is used, i.e. heat flow in repeated element, which consists of one fibre in the matrix, is considered. It leads to 2-D nonlinear boundary value problems in matrix and fibre regions. In the paper, it is proposed to solve the given nonlinear boundary value problem by Picard iteration. For every iteration step, the linear boundary value problem with two uncoupled linear partially differential equations and coupled boundary conditions is solved. The method of fundamental solution, supported by radial basis functions approximation, is implemented to obtain the required solutions. The numerical experiment has been performed. The results of the experiment and some conclusions are included as well.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2011.09.016