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
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)
I. M. Abdurakhmanov, Inzh.-Fiz. Zh.,22, No. 4 (1972).
M. A. Lavrent'ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variables [in Russian], Fizmatgiz, Moscow (1973).
A. Gurvits and R. Kurant, Theory of Functions [in Russian], Fizmatgiz, Moscow (1968).
I. M. Abdurakhmanov and B. G. Alibekov, Inzh.-Fiz. Zh.,32, No. 3 (1977).
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
- Statistical Physic
- Temperature Field
- Complex Potential
- Integrodifferential Equation
- Plane Temperature