Skip to main content
Log in

Nonstationary temperature fields in an isotropic half-space under mixed boundary conditions characteristic of technologies of laser therapy in medicine

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

Abstract

For the first time, the solution of the heat-conduction equation with mixed boundary conditions (BCs) is obtained as applied to the model of an isotropic nontransparent half-space, whose surface z = 0 is heated through the circular region of radius r = R with a heat-flux density characteristic of a laser heat source, while outside of the circle of r > R and z = 0 there occurs intense cooling at the value of the heat-transfer coefficient α = ∞.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

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

  2. J. V. Beck,Int. J. Heat Mass Transfer,24, 155–164 (1981).

    Article  Google Scholar 

  3. V. P. Kozlov,Two-Dimensional Axially Symmetric Nonstationary Heat-Conduction Problems [in Russian], Minsk (1986).

  4. V. P. Kozlov,Inzh.-Fiz. Zh.,54, No. 3, 484–493 (1988).

    Google Scholar 

  5. D. O’Shea, R. Collen, and U. Rods,Laser Technology [Russian translation], Moscow (1980).

  6. N. A. Abdel’razak,Methods of Solving Two-Dimensional Problems of Nonstationary Heat-Conduction with Mixed and Unmixed Discontinuous Boundary Conditions. Author’s Abstract of Candidate’s Dissertation in Physical-Mathematical Sciences, Minsk (1996).

    Google Scholar 

  7. V. P. Kozlov, N. I. Yurchuk, and P. A. Mandrik,Inzh.-Fiz. Zh,71, No. 4, 734–743 (1998).

    Google Scholar 

  8. V. P. Kozlov, N. I. Yurchuk, and P. A. Mandrik,Vestn. Belorus. Univ., Ser. 1, No. 2, 37–42 (1999).

  9. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev,Integrals and Series. Special Functions [in Russian], Moscow (1983).

  10. G. M. Fikhtengol’ts,A Course in Differential and Integral Calculus [in Russian], Vol. 2, Moscow (1966).

  11. M. Abramovits and I. Stigan (eds.),Handbook of Special Functions [Russian translation], Moscow (1979).

  12. G. Bateman and A. Erdélyi,Tables of Integral Transformations, Vol. 1,Fourier, Laplace, and Mellin Transforms [in Russian], Moscow (1969).

  13. Ya. S. Uflyand,Method of Paired Equations in Mathematical Physics Problems [in Russian], Leningrad (1977).

  14. I. Sneddon,Mixed Boundary-Value Problems in Potential Theory, Amsterdam (1966).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 3, pp. 637–644, May–June, 2000.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kozlov, V.P., Mandrik, P.A. Nonstationary temperature fields in an isotropic half-space under mixed boundary conditions characteristic of technologies of laser therapy in medicine. J Eng Phys Thermophys 73, 625–633 (2000). https://doi.org/10.1007/BF02681807

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02681807

Keywords

Navigation