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On a Fundamental Solution to Problems of Electrostatics and Heat Conductunce for Plane-Layered Media

  • HEAT AND MASS TRANSFER AND PHYSICAL GASDYNAMICS
  • Published:
High Temperature Aims and scope

Abstract

The article studies the electrostatic field from a point charge inside or outside a plane-layered medium (a fundamental solution to the problem of electrostatics for plane-layered media). For arbitrary plane-layered media, a solution to the problem is obtained in the form of a one-dimensional integral. Based on the analogy between electrostatics and heat conductunce, the application of the obtained electrostatic solutions to heat conductunce problems is considered.

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REFERENCES

  1. Pollack, H.N., J. Geophys. Res., 1965, vol. 70, no. 22, p. 5645.

    Article  ADS  Google Scholar 

  2. Negi, J.G. and Singh, R.N., Pure Appl. Geophys., 1969, vol. 73, no. 1, p. 143.

    Article  ADS  Google Scholar 

  3. Negi, J.G. and Singh, R.N., Pure Appl. Geophys., 1968, vol. 69, no. 1, p. 110.

    Article  ADS  Google Scholar 

  4. Matysiak, S.J. and Perkowski, D.M., Heat Mass Transfer, 2014, vol. 50, no. 1, p. 75.

    Article  ADS  Google Scholar 

  5. Chew, W.C., Waves and Fields in Inhomogeneous Media, New York: IEEE, 1995.

    Google Scholar 

  6. Petrin, A.B., Opt. Spectrosc., 2020, vol. 128, no. 11, p. 1809.

    Article  ADS  Google Scholar 

  7. Petrin, A.B., Opt. Spectrosc., 2021, vol. 129, no. 1, p. 56.

    Article  ADS  Google Scholar 

  8. Petrin, A.B., J. Exp. Theor. Phys., 2021, vol. 132, no. 1, p. 27.

    Article  ADS  Google Scholar 

  9. King, R.W.P. and Smith, G.S., Antennas in Matter, Cambridge: Cambridge Univ. Press, 1981.

    Google Scholar 

  10. King, R.W.P., IEEE Trans. Microwave Theory Tech., 1988, vol. 36, no. 6, p. 1080.

    Article  ADS  Google Scholar 

  11. Petrin, A.B., Opt. Spectrosc., 2021, vol. 129, no. 1, p. 72.

    Article  ADS  Google Scholar 

  12. Gradshtein, I.S. and Ryzhik, I.M., Tablitsy integralov, summ, ryadov i proizvedenii (Tables of Integrals, Sums, Series, and Products), Moscow: Fizmatgiz, 1963, 4th ed.

  13. Sivukhin, D.V., Obshchii kurs fiziki. Uchebnoe posobie (General Physics: Textbook), vol. 3: Elektrichestvo (Electricity), Moscow: Fizmatlit, 2004, 4th ed.

  14. Petrin, A.B., Opt. Spectrosc., 2021, vol. 129, no. 1, p. 72.

    Article  ADS  Google Scholar 

  15. Feynman, R.P., Leighton, R.B., and Sands, M., The Feynman Lectures on Physics, vol. 5: Electricity and Magnetism, New York: Addison-Wesley, 1964.

    Google Scholar 

  16. Landau, L.D. and Lifshits, E.M., Teoreticheskaya fizika (Theoretical Physics), vol. 6: Gidrodinamika (Fluid Dynamics), Moscow: Nauka, 1986.

  17. Kartashov, E.M., Analiticheskie metody v teorii teploprovodnosti tverdykh tel (Analytical Methods in the Theory of Heat Conductunce of Solids), Moscow: Vysshaya Shkola, 2001.

  18. Petrin, A.B., High Temp., 2018, vol. 56, no. 2, p. 157.

    Article  Google Scholar 

  19. Petrin, A.B., Usp. Prikl. Fiz., 2016, vol. 4, no. 4, p. 326.

    Google Scholar 

  20. Kartashov, E.M., Kudinov, V.A., and Kalashnikov, V.V., Teoriya teplomassoperenosa: reshenie zadach dlya mnogosloinykh konstruktsii: uchebnoe posobie (Theory of Heat and Mass Transfer: Solving Problems for Multilayer Structures: A Textbook), Kartashov, E.M, Ed., Moscow: Yurait, 2018.

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  1. Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, Russia

    A. B. Petrin

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Correspondence to A. B. Petrin.

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Petrin, A.B. On a Fundamental Solution to Problems of Electrostatics and Heat Conductunce for Plane-Layered Media. High Temp 60, 677–687 (2022). https://doi.org/10.1134/S0018151X22040058

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