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Construction of “on the average exact” asymptotic solution of the problem on radial distribution of temperature field in a well

  • Heat and Mass Transfer and Physical Gasdynamics
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High Temperature Aims and scope

Abstract

The example of the problem on radial distribution of temperature field in a well is used to illustrate the application of a modification of the asymptotic method for solving a number of problems in subterranean thermodynamics. The problem is represented in the form of a set of equations of mixed types for the respective coefficients of expansion, remainder term, and boundary-layer functions. Analytical expressions are constructed for coefficients of zero-order and first-order expansion and for boundary-layer functions. It is demonstrated that the constructed asymptotic formula provides for vanishing of the solution of the averaged problem for remainder term.

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References

  1. Filippov, A.I., Mikhailov, P.N., and Akhmetova, O.V., Teplofiz. Vys. Temp., 2006, vol. 44, no. 5, p. 747 (High Temp. (Engl. transl.), vol. 44, no. 5, p. 743).

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  3. Filippov, A.I., Mikhailov, P.N., and Akhmetova, O.V., Mathematical Simulation of Temperature Field in a Well in View of Radial Profile of Velocity, in Matematicheskie metody v tekhnike i tekhnologiyakh. MMTT-17: Sbornik trudov XVII Mezhdunarodnoi nauchnoi konferentsii, T. 1 (Mathematical Methods in Engineering and Technologies. MMTT-17: Proceedings of XVII International Scientific Conference), Kostroma: Izd. Kostroma State Technological Univ., 2004, vol. 1, p. 84.

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Authors and Affiliations

  1. Sterlitamak Division of the Academy of Sciences of the Republic of Bashkortostan, Sterlitamak, Bashkortostan, 453103, Russian Federation

    A. I. Filippov, P. N. Mikhailov, O. V. Akhmetova & M. A. Goryunova

Authors
  1. A. I. Filippov
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  2. P. N. Mikhailov
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  3. O. V. Akhmetova
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  4. M. A. Goryunova
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Additional information

Original Russian Text © A.I. Filippov, P.N. Mikhailov, O.V. Akhmetova, M.A. Goryunova, 2008, published in Teplofizika Vysokikh Temperatur, Vol. 46, No. 3, 2008, pp. 449–456.

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Filippov, A.I., Mikhailov, P.N., Akhmetova, O.V. et al. Construction of “on the average exact” asymptotic solution of the problem on radial distribution of temperature field in a well. High Temp 46, 406–413 (2008). https://doi.org/10.1134/S0018151X08030188

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  • DOI: https://doi.org/10.1134/S0018151X08030188

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