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Direct and inverse heat-conduction problems for a semiinfinite rod for a partial outflow of heat through the surface

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Abstract

Analytical solutions of the direct and inverse problems of nonstationary heat conduction in a thin semiinfinite rod are given for the case of radiative heat fluxes at the lateral surfaces and a partial outflow of heat by convection and radiation through the end of the rod.

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Abbreviations

α:

thermal diffusivity

x1 :

coordinate along the length of the rod

t1 :

time

t=αt1/d2 :

dimensionless time (Fourier number)

x=X1/d:

relative coordinate

To :

initial temperature

σ:

Boltzmann constant

Sk=ɛαaTc 3d/λ:

Stark number

Bi=αd/λ:

reduced Biot number

ɛ:

emissivity

Literature cited

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  3. A. N. Tikhonov, “On the cooling of a body with radiative emission given by the Stefan-Boltzman law,” Izv. Akad. Nauk Geogr. Geofiz., No. 3, 461–479 (1937).

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  4. B. A. Grigor'ev, V. A. Nuzhnyi, and V. V. Shibanov, Tables for Calculating the Nonstationary Temperature of Planar Bodies with Heating by Radiation [in Russian], Nauka, Moscow (1971).

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

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  6. P. V. Tsoi, “Nonstationary heat exchange in systems of bodies,” Inzh.-Fiz. Zh.,47, No. 1, 120–124 (1961).

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Authors and Affiliations

  1. Tadjik Polytechnic Institute, Dushanbe

    P. V. Tsoi, S. Yu. Yusunov & N. R. Korpeev

Authors
  1. P. V. Tsoi
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  2. S. Yu. Yusunov
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  3. N. R. Korpeev
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Additional information

Translated from Inzhenero-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 148–153, July, 1984.

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Tsoi, P.V., Yusunov, S.Y. & Korpeev, N.R. Direct and inverse heat-conduction problems for a semiinfinite rod for a partial outflow of heat through the surface. Journal of Engineering Physics 47, 860–864 (1984). https://doi.org/10.1007/BF00832608

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  • DOI: https://doi.org/10.1007/BF00832608

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