A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam
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 ar...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2012-06-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20899/17158 |
| _version_ | 1811330197369126912 |
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| author | Victor V Manako |
| author_facet | Victor V Manako |
| author_sort | Victor V Manako |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T15:58:07Z |
| format | Article |
| id | doaj.art-32ee1186850949a3ba569e39b68b441b |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T15:58:07Z |
| publishDate | 2012-06-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-32ee1186850949a3ba569e39b68b441b2022-12-22T02:40:37ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812012-06-0116211512318316A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beamVictor V Manako0Samara State Technical UniversityWe 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.https://journals.eco-vector.com/1991-8615/article/viewFile/20899/17158heat conductivity boundary value problemcircular heat sourcehypergeometric series |
| spellingShingle | Victor 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 Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki heat conductivity boundary value problem circular heat source hypergeometric series |
| title | A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam |
| title_full | A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam |
| title_fullStr | A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam |
| title_full_unstemmed | A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam |
| title_short | A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam |
| title_sort | representation in terms of hypergeometric functions for the temperature field in a semi infinite body that is heated by a motionless laser beam |
| topic | heat conductivity boundary value problem circular heat source hypergeometric series |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20899/17158 |
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