A Mathematical Theorem on the Onset of Stationary Convection in Couple-Stress Fluid
The thermal instability of a couple-stress fluid heated from below is investigated. Following the linearized stability theory and normal mode analysis, the paper mathematically establishes that the onset of instability at marginal state, cannot manifest itself as stationary convection, if the ther...
| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Isfahan University of Technology
2013-01-01
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| Series: | Journal of Applied Fluid Mechanics |
| Subjects: | |
| Online Access: | http://jafmonline.net/JournalArchive/download?file_ID=26995&issue_ID=212 |
| _version_ | 1818352916486946816 |
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| author | Banyal Ajaib Singh |
| author_facet | Banyal Ajaib Singh |
| author_sort | Banyal Ajaib Singh |
| collection | DOAJ |
| description | The thermal instability of a couple-stress fluid heated from below is investigated. Following the linearized stability
theory and normal mode analysis, the paper mathematically establishes that the onset of instability at marginal state,
cannot manifest itself as stationary convection, if the thermal Rayleigh number R and the couple-stress parameter F,
3
satisfy the inequality
2 2
2
2 1 3 F 3 F 1 3 F 1
, and when the couple-stress parameter F is
R
2
2
27 F 1 1 3 F
infinitesimally small, R
27 4
4
2
F , the result which also clearly mathematically established the stabilizing
1
2
character of the couple-stress. |
| first_indexed | 2024-12-13T19:01:14Z |
| format | Article |
| id | doaj.art-aaf813ce50274b63b113e39020ec1764 |
| institution | Directory Open Access Journal |
| issn | 1735-3645 |
| language | English |
| last_indexed | 2024-12-13T19:01:14Z |
| publishDate | 2013-01-01 |
| publisher | Isfahan University of Technology |
| record_format | Article |
| series | Journal of Applied Fluid Mechanics |
| spelling | doaj.art-aaf813ce50274b63b113e39020ec17642022-12-21T23:34:41ZengIsfahan University of TechnologyJournal of Applied Fluid Mechanics1735-36452013-01-0162191196.A Mathematical Theorem on the Onset of Stationary Convection in Couple-Stress FluidBanyal Ajaib Singh0NSCBM, Govt. College Hamirpur (HP) India 177001The thermal instability of a couple-stress fluid heated from below is investigated. Following the linearized stability theory and normal mode analysis, the paper mathematically establishes that the onset of instability at marginal state, cannot manifest itself as stationary convection, if the thermal Rayleigh number R and the couple-stress parameter F, 3 satisfy the inequality 2 2 2 2 1 3 F 3 F 1 3 F 1 , and when the couple-stress parameter F is R 2 2 27 F 1 1 3 F infinitesimally small, R 27 4 4 2 F , the result which also clearly mathematically established the stabilizing 1 2 character of the couple-stress.http://jafmonline.net/JournalArchive/download?file_ID=26995&issue_ID=212Thermal convection; Couple-stress fluid; Rayleigh number. |
| spellingShingle | Banyal Ajaib Singh A Mathematical Theorem on the Onset of Stationary Convection in Couple-Stress Fluid Journal of Applied Fluid Mechanics Thermal convection; Couple-stress fluid; Rayleigh number. |
| title | A Mathematical Theorem on the Onset of Stationary Convection in Couple-Stress Fluid |
| title_full | A Mathematical Theorem on the Onset of Stationary Convection in Couple-Stress Fluid |
| title_fullStr | A Mathematical Theorem on the Onset of Stationary Convection in Couple-Stress Fluid |
| title_full_unstemmed | A Mathematical Theorem on the Onset of Stationary Convection in Couple-Stress Fluid |
| title_short | A Mathematical Theorem on the Onset of Stationary Convection in Couple-Stress Fluid |
| title_sort | mathematical theorem on the onset of stationary convection in couple stress fluid |
| topic | Thermal convection; Couple-stress fluid; Rayleigh number. |
| url | http://jafmonline.net/JournalArchive/download?file_ID=26995&issue_ID=212 |
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