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Conductivity of a periodic particle composite with transversely isotropic phases. (English) Zbl 0888.73037

The main goal is to calculate the effective conductivity tensor of a composite with transversely isotropic phases. The problem is reformulated as the following conjugation problem: Find a function \(T(x,y,z)\) sectionally harmonic and triple-periodic in \(\mathbb{R}^3\) with the boundary conditions \(T^+-T^-=0\), \({\mathbf q}^+ {\mathbf n}- {\mathbf q}^- {\mathbf n}= 0\) on \(S\), where \({\mathbf q}= -\Lambda \nabla T\), \(\Lambda\) is a symmetric matrix, and \(S\) is the boundary surface of a spheroid. The classical Fourier series method and the addition theorem method are used to reduce the problem to an infinite set of linear algebraic equations. Numerical results are presented.

MSC:

74E30 Composite and mixture properties
80A20 Heat and mass transfer, heat flow (MSC2010)
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