Skip to main content
SpringerLink
Log in

A method to determine a body’s thermal state

  • Mining Thermophysics
  • Published:
Journal of Mining Science Aims and scope

Abstract

Given the known temperature and its gradient at a body’s boundary, the heat distribution, including the location and geometry of heat sources in the body interiorбis recovered. The article analyzes the plane stationary problem formulation and solution, and the Hadamard’s example. The proposed scheme of numerical solution (with an option of extension for 3D case) is compared with the analytical solution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Tikhonov, A.N. and Samarsky A.A., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1977.

    Google Scholar 

  2. Courant, R. and Hilbert, D., Methods of Mathematical Physics: Partial Differential Equations, John Wiley, 1961.

  3. Vladimirov, V.S., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1971.

    Google Scholar 

  4. Haberman, R., Elementary Applied Partial Differential Equations, New Jersey: A Paramount Communications Company Englewood Cliffs, 1987.

    Google Scholar 

  5. Muskhelishvili, N.N., Nekotorye osnovnye zadachi matematicheskoi teorii uprogosti (Some Principal Problems of Mathematical Elastic Theory), Novosibirsk: Nauka, 2009.

    Google Scholar 

  6. Kabanikhin, S.I., Obratnye i nekorrektnye zadachi (Inverse and Ill-Posed Problems), Novosibirsk: Nauka, 2009.

    Google Scholar 

  7. Sobolev, S.L., Uravneniya matematicheskoi fiziki (Equations of Mathematical Physics), Moscow: Nauka, 1966.

    Google Scholar 

  8. Shvab, A.A., “Inverse Overspecified Problem for Inhomogeneous Elastic Medium,” Sib. Zh. Industr. Matem., 2004, vol. 7, no. 4.

  9. Chanyshev, A.I. and Vologin, D.A., “Determination of the Stress-Strain State and Damages in a Rock Mass by the Displacement Measurement on Its Surface. Part I: Analytical Solutions,” Journal of Mining Science, 2012, vol. 47, no. 4, pp. 395–403.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. N.A. Chinakal Institute of Mining, Siberian Branch, Russian Academy of Sciences, Krasnyi pr. 54, Novosibirsk, 630091, Russia

    A. I. Chanyshev

Authors
  1. A. I. Chanyshev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.I. Chanyshev, 2012, published in Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, 2012, No. 4, pp. 83–93

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chanyshev, A.I. A method to determine a body’s thermal state. J Min Sci 48, 660–668 (2012). https://doi.org/10.1134/S1062739148040107

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1062739148040107

Key words

Search

Navigation