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Duhamel integral and the operational-structural method of solution in nonstationary heat-conduction problems for regions of complicated shape

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Abstract

We propose an analytic method for solving nonstationary heat-conduction problems for regions of complicated shape with nonstationary boundary conditions and energy sources.

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Abbreviations

u:

temperature

ρ:

density

λ:

thermal conductivity

c:

specific heat capacity

n:

number of coordinate functions

Fo=t(λ/ρcL):

Fourier number

ν :

direction of the inner normal to the contour Г2

L:

characteristic dimension of the plate

d:

thickness of the plate

α:

sum of the total heat-transfer coefficients from the surface of the plate

Bi=αL2/λd=b2 :

Biot number

Literature cited

  1. V. L. Rvachev and A. P. Slesarenko, The Algebra of Logic and Integral Transforms in Boundary-Value Problems [in Russian], Naukova Dumka, Kiev (1976).

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

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  3. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Oxford Univ. Press (1959).

  4. V. A. Ditkin and A. P. Prudnikov, Integral Transforms and Operational Calculus [in Russian], Nauka, Moscow (1974).

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  5. S. G. Mikhlin, Variational Methods in Mathematical Physics [in Russian], Nauka, Moscow (1970).

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Author information

Authors and Affiliations

  1. Machine Design Problems Institute, Academy of Sciences of the Ukrainian SSR, Kharkov

    A. P. Slesarenko & A. I. Luzan

  2. Kharkov State Scientific-Research Institute of Metrology, USSR

    A. P. Slesarenko & A. I. Luzan

Authors
  1. A. P. Slesarenko
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  2. A. I. Luzan
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Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 901–906, May, 1981.

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Slesarenko, A.P., Luzan, A.I. Duhamel integral and the operational-structural method of solution in nonstationary heat-conduction problems for regions of complicated shape. Journal of Engineering Physics 40, 560–565 (1981). https://doi.org/10.1007/BF00822127

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  • DOI: https://doi.org/10.1007/BF00822127

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