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Transport properties of a rectangular array of highly conducting cylinders

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Abstract

The method of functional equations is applied to evaluate the effective conductivity tensor for a rectangular array of highly conducting cylinders. The Rayleigh sum S 2 is calculated by Eisenstein and Weierstrass functions. Approximate analytical formula for the effective conductivity tensor are deduced.

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References

  1. Lord Rayleigh, On the influence of obstacles arranged in rectangular order upon the properties of a medium. Phil. Mag. 34 (1892) 481-502.

    Google Scholar 

  2. R. C. McPhedran and G. Milton, Bounds and exact theories for the transport properties of inhomogeneous media. Appl. Phys. A26 (1981) 207-220.

    Google Scholar 

  3. R. C. McPhedran, Transport properties of cylinder pairs and the square array of cylinders. Proc. R. Soc. London A408 (1986) 31-43.

    Google Scholar 

  4. R. C. McPhedran and G. Milton, Transport properties of touching cylinder pairs and of the square array of touching cylinders. Proc. R. Soc. London A411 (1987) 313-326.

    Google Scholar 

  5. R. C. McPhedran, L. Poladian and G. Milton, Asymptotic studies of closely spaced, highly conducting cylinders. Proc. R. Soc. London A415 (1988) 185-196.

    Google Scholar 

  6. W. T. Perrins, D. R. McKenzie and R. C. McPhedran, Transport properties of regular array of cylinders. Proc. R. Soc. London A369 (1979) 207-225.

    Google Scholar 

  7. A. S. Sangani and C. Yao, Transport properties in random arrays of cylinders. 1. Thermal conduction. Phys. Fluids 31 (1988) 2426-2434.

    Google Scholar 

  8. D. J. Bergman, The dielectric constant of a composite material-a problem in a classical physics. Phys. Reports C43 (1983) 378-407.

    Google Scholar 

  9. D. J. Bergman and K. J. Dunn, Bulk effective dielectric constant of a composite with a periodic microgeometry. Phys. Rev. B45 (1992) 13262-13271.

    Google Scholar 

  10. K. E. Clark and G. W. Milton, Optimal bounds correlating electric, magnetic and thermal properties of two-phase, two-dimensional composites. Proc. R. Soc. London A448 (1995) 161-190.

    Google Scholar 

  11. J. Kolodziej, Calculation of the effective thermal conductivity of a composite with parallel cylinders by the method of collocation. Mech. Teoret. i Stosowana 23 (1985) 355-373 (in Polish).

    Google Scholar 

  12. J. Kolodziej, Calculation of the effective thermal conductivity of a unidirectional composites. Arch. Termodynamiki 8 (1987) 101-107 (in Polish).

    Google Scholar 

  13. V. V. Mityushev, Steady heat conduction of two-dimensional composites. Proc. IX Symp. Heat Mass Transfer, Augustow. 2 (1995) 93-100.

    Google Scholar 

  14. V. V. Mityushev, Transport properties of double-periodic arrays of circular cylinders. ZAMM 77 (1997) 115-120.

    Google Scholar 

  15. V. V. Mityushev, Functional equations in a class of analytic functions and composite materials. Demonstratio Mathematica 30 (1997) 63-70.

    Google Scholar 

  16. V. V. Mityushev, Rayleigh's integral and the square array of cylinders. Arch. Mech. 47 (1995) 27-37.

    Google Scholar 

  17. V. V. Mityushev, A method of functional equations for boundary value problems of continuous media. Reports Math. Phys. 33 (1993) 137-147.

    Google Scholar 

  18. V. V. Mityushev, Application of Functional Equation to Determination of the Effective Thermal Conductivity of Composite Materials. Slupsk: WSP (1996) 155 pp (in Polish).

    Google Scholar 

  19. V. V. Mityushev, Finite and infinite composite materials and Rayleigh's sum. Arch. Mech. 49 (1997) 345-358.

    Google Scholar 

  20. A. Weil, Elliptic Functions According to Eisenstein and Kronecker. Berlin: Springer-Verlag (1976) 112 pp.

    Google Scholar 

  21. A. Hurwitz and R. Courant, Allgemeine Funktionentheorie und Elliptische Funktionen. Berlin: Springer-Verlag (1964) 274 pp.

    Google Scholar 

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Rylko, N. Transport properties of a rectangular array of highly conducting cylinders. Journal of Engineering Mathematics 38, 1–12 (2000). https://doi.org/10.1023/A:1004669705627

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