Email this article A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam
- Authors: Manako V.V1
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Affiliations:
- Samara State Technical University
- Issue: Vol 16, No 2 (2012)
- Pages: 115-123
- Section: Articles
- URL: https://journals.eco-vector.com/1991-8615/article/view/20899
- ID: 20899
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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.
About the authors
Victor V Manako
Samara State Technical University
Email: viktor.manako@mail.ru
(к.ф.-м.н., доц.), доцент, каф. общей физики и физики нефтегазового производства; Самарский государственный технический университет; Samara State Technical University
References
- Пинскер В. А. Нестационарное температурное поле в полуограниченном теле, нагреваемом круговым поверхностным источником тепла // Теплофизика высоких температур, 2006. Т. 44, № 1. С. 127-135.
- Appel P., Kampé de Fériet J. Fonctions Hypergéométriques et Hypersphériques. Polynômes d'Hermite. Paris: Gauthier-Villars, 1926. 202 pp.
- Srivastava H. M., Manocha H. L. A treatise on generating functions. New York: Halsted Press [John Wiley & Sons, Inc.], 1984. 569 pp.
- Carslaw H. S., Jaeger J. C. Conduction of Heat in Solids. Oxford: Clarendon Press, 1959. 510 pp.
- Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables / eds. M. Abramowitz, I. A. Stegun. New York: Dover, 1972. 824 pp.
- Прудников А. П., Брычков Ю. А., Маричев О. И. Интегралы и ряды. Т. 3: Специальные функции. Дополнительные главы. М.: Физматлит, 2003. 688 с.
- Манако В. В., Путилин В. А., Камашев А. В. Расчет температуры при нагреве неподвижным лазерным лучом // Теплофизика высоких температур, 2011. Т. 49, № 1. С. 126-132.
- Srivastava H. M., Miller E. A. A unified presentation of the Voigt functions // Astrophys. and Space Sci., 1987. Vol. 135, no. 1. Pp. 111-118.
