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Effect of a biperiodic system of plane inclusions on a plane steady temperature field

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Determining the complex potential of a plane temperature field perturbed by a biperiodic system of thin inclusions reduces to the solution of a singular integrodifferential equation.

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T+ and T :

values of the temperature T at the left-hand and right-hand edges of the inclusion


current function


complex potential of temperature field unperturbed by inclusions


complex potential of temperature field perturbed by inclusions

k0 and k:

thermal conductivity of the inclusions and the body

Γn :

smooth line in the complex z plane


piecewise continuous line

2h0 :

width of the inclusion

2ω and 2ω′ :

periods of complex potential W(z)


source strength

Literature cited

  1. 1.

    I. M. Abdurakhmanov, Inzh.-Fiz. Zh.,22, No. 4 (1972).

  2. 2.

    M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variables [in Russian], Fizmatgiz, Moscow (1973).

  3. 3.

    A. Gurvits and R. Kurant, Theory of Functions [in Russian], Fizmatgiz, Moscow (1968).

  4. 4.

    I. M. Abdurakhmanov and B. G. Alibekov, Inzh.-Fiz. Zh.,32, No. 3 (1977).

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Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 930–934, November, 1978.

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Abdurakhmanov, I.M., Alibekov, B.G. Effect of a biperiodic system of plane inclusions on a plane steady temperature field. Journal of Engineering Physics 35, 1383–1387 (1978). https://doi.org/10.1007/BF00859696

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  • Statistical Physic
  • Temperature Field
  • Complex Potential
  • Integrodifferential Equation
  • Plane Temperature