Kushch, V. I. Conductivity of a periodic particle composite with transversely isotropic phases. (English) Zbl 0888.73037 Proc. R. Soc. Lond., Ser. A 453, No. 1956, 65-76 (1997). 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. Reviewer: V.Mityushev (Słupsk) Cited in 8 Documents MSC: 74E30 Composite and mixture properties 80A20 Heat and mass transfer, heat flow (MSC2010) Keywords:boundary value problem; sectionally harmonic triple-periodic function; effective conductivity tensor; conjugation problem; symmetric matrix; spheroid; Fourier series method; addition theorem method; infinite set of linear algebraic equations PDFBibTeX XMLCite \textit{V. I. Kushch}, Proc. R. Soc. Lond., Ser. A 453, No. 1956, 65--76 (1997; Zbl 0888.73037) Full Text: DOI