Skip to main content
SpringerLink
Log in

Determination of heat transfer properties of media with a single-needle probe

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

Needle probes with a line heater inside are often used in studying the heat transfer properties of loose rocks. The key problem of contact methods of measuring thermal properties of various media consists in finding thermal contact resistance at the probe/medium interface which must be taken into account in determining the thermal diffusivity of the medium. We describe a mathematical model of heating of a long needle probe in the medium under study, taking into account dimensions and thermal properties of the needle source and assuming that thermal contact between the source and the medium is not ideal. Based on the proposed model, we formulate and solve the inverse problem of finding the thermal diffusivity coefficient of the medium and the heat exchange coefficient at the probe/medium interface. The purpose of the article is to create methodology for determining thermal properties of various media in the field.

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. V. V. Babaev, V.F. Budymka, M. A. Dombrovskii, et al., Thermal Properties of Rocks (Nedra, Moscow, 1987) [in Russian].

    Google Scholar 

  2. D. R. Lide, CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, 2009).

    Google Scholar 

  3. R. Von Herzen and A. E. Maxwell, “TheMeasurement of Thermal Conductivity of Deep Sea Sediments by a Needle ProbeMethod,” J. Geophys. Research 64 (10), 1557–1563 (1959).

    Article  Google Scholar 

  4. J. H. Blackwell, “A Transient-FlowMethod for Determination of Thermal Constants of Insulating Materials in Bulk,” J. Appl. Phys. 25 (2), 137–144 (1954).

    Article  MATH  Google Scholar 

  5. W. F. Waite et al. “Sumultaneous Determination of Thermal Conductivity, Thermal Diffusivity, and Specific heat in SI Methane Hydrate,” Geophys. J. Internat. 169, 767–774 (2007).

    Article  Google Scholar 

  6. S. A. Kazantsev and I. I. Fadeeva, “A Device for Executive Measurement of Thermal Diffusivity of Incompetent Rocks,” in International Scientific Conference “Subsoil Use. Mining. Directions and Technologies of Search, Exploration, and Development of Deposits of Minerals. Geoecology”, Vol. 2 (Sibir. Gos. Univ. Geosystem i Tekhnol., Novosibirsk, 2015), pp. 82–85.

    Google Scholar 

  7. I. I. Fadeeva, A. A. Duchkov, and A. L. Karchevsky, “Theory of the Needle Probe Method for Simultaneous Determination of the Thermal Conductivity and the Thermal Diffusivity of Various Media,” Interexpo Geo-Sibir’ 2 (3), 118–122 (2014).

    Google Scholar 

  8. O. M. Alifanov, E. A. Artyukhin, and S. V. Rumyantsev, ExtremeMethods for Solving Ill-Posed Problems with Applications to Universe Heat Transfer Problems (Begell House, New York, 1995).

    MATH  Google Scholar 

  9. A. L. Karchevsky, “Analysis of Solving of the Inverse Dynamical Problem of Seismics for Horisontally Stratified AnisotropicMedia,” Russ. Geology and Geophysics 47 (11), 1150–1164 (2006).

    Google Scholar 

  10. A. L. Karchevsky, “Simultaneous Reconstruction of Permittivity and Conductivity,” J. Inverse Ill-Posed Probl. 17 (4), 385–402 (2009); DOI 10.1515/JIIP.2009.026.

    Article  MathSciNet  MATH  Google Scholar 

  11. A. A. Duchkov and A. L. Karchevsky, “Determination of Terrestrial Heat Flow from Temperature Measurements in Bottom Sediments,” Sibir. Zh. Industr. Mat. 16 (3), 61–85 (2013) [J. Appl. Indust. Math. 7 (4), 480–502 (2013)].

    MATH  Google Scholar 

  12. L. A. Nazarova, L. A. Nazarov, A. L. Karchevsky, and M. Vandamme, “Estimating Diffusion-Capacity Parameters of a Coal Bed Using the Gas Pressure Measured in a Hole and the Solution of an Inverse Problem,” Sibir.Zh. Industr. Mat. 17 (1), 78–85 (2014) [J. Appl. Indust. Math. 8 (2), 267–273 (2014)].

    MATH  Google Scholar 

  13. A. L. Karchevsky, “Reconstruction of Pressure Velocities and Boundaries of Thin Layers in Thinly-Stratified Layers,” J. Inverse Ill-Posed Probl. 18 (4), 371–388 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  14. A. I. Volkov and I. M. Zharskii, Great Chemical Handbook (Sovremennaya Shkola, Minsk, 2005) [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chinakal Institute of Mining, Krasnyi pr. 54, Novosibirsk, 630091, Russia

    I. I. Fadeeva

  2. Trofimuk Institute of Oil-and-Gas Geology and Geophysics, pr. Akad. Koptyuga 3, Novosibirsk, 630090, Russia

    I. I. Fadeeva & A. A. Duchkov

  3. Novosibirsk State Technical University, pr. Karla Marksa 20, Novosibirsk, 630073, Russia

    A. A. Duchkov

Authors
  1. I. I. Fadeeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Duchkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. I. Fadeeva.

Additional information

Original Russian Text © I.I. Fadeeva, A.A. Duchkov, 2017, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2017, Vol. XX, No. 4, pp. 80–89.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fadeeva, I.I., Duchkov, A.A. Determination of heat transfer properties of media with a single-needle probe. J. Appl. Ind. Math. 11, 506–513 (2017). https://doi.org/10.1134/S199047891704007X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S199047891704007X

Keywords

Search

Navigation