Piecewise uniform optimal design of a bar with an attached mass
We minimize, with respect to the cross sectional area, the mass of a bar given the rate of heat transfer. The bar enhances the heat transfer surface of a larger known mass to which the bar is attached. This article is an extension of a previous publication by two coauthors, where heat transfer...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-08-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/206/abstr.html |
| _version_ | 1818512547975790592 |
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| author | Boris P. Belinskiy James W. Hiestand John V. Matthews |
| author_facet | Boris P. Belinskiy James W. Hiestand John V. Matthews |
| author_sort | Boris P. Belinskiy |
| collection | DOAJ |
| description | We minimize, with respect to the cross sectional area, the mass of a
bar given the rate of heat transfer. The bar enhances the heat transfer
surface of a larger known mass to which the bar is attached.
This article is an extension of a previous publication by two coauthors,
where heat transfer from the sides of the bar was neglected and only
conduction through its length was considered. The rate of cooling is
defined by the first eigenvalue of the corresponding Sturm-Liouville problem.
We compare the mass of the computed variable cross-section bar with the mass
of a bar with constant cross-sectional area and the same rate of heat transfer,
and conclude that a fin design with constant, or near constant, cross-sectional
area is best. |
| first_indexed | 2024-12-10T23:48:23Z |
| format | Article |
| id | doaj.art-aebab4466ae744f1ba4722cd0bbf1193 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T23:48:23Z |
| publishDate | 2015-08-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-aebab4466ae744f1ba4722cd0bbf11932022-12-22T01:28:51ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-08-012015206,117Piecewise uniform optimal design of a bar with an attached massBoris P. Belinskiy0James W. Hiestand1John V. Matthews2 Univ. of Tennessee, Chattanooga,TN, USA Univ. of Tennessee, Chattanooga,TN, USA Univ. of Tennessee, Chattanooga,TN, USA We minimize, with respect to the cross sectional area, the mass of a bar given the rate of heat transfer. The bar enhances the heat transfer surface of a larger known mass to which the bar is attached. This article is an extension of a previous publication by two coauthors, where heat transfer from the sides of the bar was neglected and only conduction through its length was considered. The rate of cooling is defined by the first eigenvalue of the corresponding Sturm-Liouville problem. We compare the mass of the computed variable cross-section bar with the mass of a bar with constant cross-sectional area and the same rate of heat transfer, and conclude that a fin design with constant, or near constant, cross-sectional area is best.http://ejde.math.txstate.edu/Volumes/2015/206/abstr.htmlOptimal designheat transferheat equationleast eigenvalueSturm-Liouville problemcalculus of variationstranscendental equationcomputer algebra |
| spellingShingle | Boris P. Belinskiy James W. Hiestand John V. Matthews Piecewise uniform optimal design of a bar with an attached mass Electronic Journal of Differential Equations Optimal design heat transfer heat equation least eigenvalue Sturm-Liouville problem calculus of variations transcendental equation computer algebra |
| title | Piecewise uniform optimal design of a bar with an attached mass |
| title_full | Piecewise uniform optimal design of a bar with an attached mass |
| title_fullStr | Piecewise uniform optimal design of a bar with an attached mass |
| title_full_unstemmed | Piecewise uniform optimal design of a bar with an attached mass |
| title_short | Piecewise uniform optimal design of a bar with an attached mass |
| title_sort | piecewise uniform optimal design of a bar with an attached mass |
| topic | Optimal design heat transfer heat equation least eigenvalue Sturm-Liouville problem calculus of variations transcendental equation computer algebra |
| url | http://ejde.math.txstate.edu/Volumes/2015/206/abstr.html |
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