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 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]: Year: Volume: Issue: Page: Find

 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2012, Issue 2(27), Pages 115–123 (Mi vsgtu1017)

Mathematical Modeling

A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam

V. V. Manako

Samara State Technical University, Samara, Russia

Abstract: We have considered an analytical expression for the temperature field of a semi-infinite body that is heated by a circular heat source located at the free surface. Unsteady temperature field is expressed in terms of the Appell and the Srivastava hypergeometric functions. We have studied some special areas in heated body where a non-stationary temperature field is expressed in terms of the Kampé de Fériet function. The obtained expressions have allowed to carry out the separation of the stationary and non-stationary parts of temperature field from each other. Calculations of the steady temperature fields generated by circular or Gaussian sources have been accomplished. Significant quantitative differences in these fields were not found.

Keywords: heat conductivity boundary value problem, circular heat source, hypergeometric series

DOI: https://doi.org/10.14498/vsgtu1017

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Bibliographic databases:

UDC: 517.588:(517.958:536.212)
PACS: 61.80.Ba
MSC: Primary 35Q80; Secondary 80A20, 33C70
Original article submitted 11/XI/2011
revision submitted – 16/IV/2012

Citation: V. V. Manako, “A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2(27) (2012), 115–123

Citation in format AMSBIB
\Bibitem{Man12} \by V.~V.~Manako \paper A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam \jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.] \yr 2012 \vol 2(27) \pages 115--123 \mathnet{http://mi.mathnet.ru/vsgtu1017} \crossref{https://doi.org/10.14498/vsgtu1017} \zmath{https://zbmath.org/?q=an:1326.35386}