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Temperature characteristics of heat exchange due to thermal conductivity of three hollow cylinders in their contact planes

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Abstract

For the case where a system of three hollow cylinders, having contact along their ends, are heated the problem on the determination of the thermal characteristics in the contact planes is solved analytically. Numerical calculations and the construction of plots of the temperature variation, thermal fluxes, and the heating and stabilization times in the contact planes are carried out on the basis of the formulas so obtained.

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Abbreviations

Θj = (Tj−T0)/(T0−Tc):

dimensionless temperature

T0 :

initial temperature

Tc :

temperature of the medium

Tj :

temperature at an arbitrary point of the j-th cylinder

Foj :

ajt/R 21

Ka :

a2/a1

d:

R2/R1

b:

R1/l

λj, aj :

thermal and thermiometric conductivities, respectively

R2, R1 :

respectively, the outer and inner radii of the cylinders

t:

time

X, Z:

dimensionless cylindrical coordinates

Literature cited

  1. A. V. Lykov, Theory of Heat Conduction [in Russian], Vysshaya Shkola, Moscow (1967).

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  2. I. Sneddon, Fourier Transforms, McGraw-Hill, New York (1951).

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Authors and Affiliations

  1. V. V. Kuibyshev Tomsk State University, USSR

    V. I. Kondrashov & V. E. Tomilov

Authors
  1. V. I. Kondrashov
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  2. V. E. Tomilov
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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 80–84, July, 1972.

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Kondrashov, V.I., Tomilov, V.E. Temperature characteristics of heat exchange due to thermal conductivity of three hollow cylinders in their contact planes. Soviet Physics Journal 15, 994–998 (1972). https://doi.org/10.1007/BF00894685

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  • DOI: https://doi.org/10.1007/BF00894685

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