Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy
A linear stability analysis has been carried out to examine the effect of internal heat source on the onset of Rayleigh–Bénard convection in a rotating nanofluid layer with double diffusive coefficients, namely, Soret and Dufour, in the presence of feedback control. The system is heated from below a...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/2789024 |
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| author | I. K. Khalid N. F. M. Mokhtar I. Hashim Z. B. Ibrahim S. S. A. Gani |
| author_facet | I. K. Khalid N. F. M. Mokhtar I. Hashim Z. B. Ibrahim S. S. A. Gani |
| author_sort | I. K. Khalid |
| collection | DOAJ |
| description | A linear stability analysis has been carried out to examine the effect of internal heat source on the onset of Rayleigh–Bénard convection in a rotating nanofluid layer with double diffusive coefficients, namely, Soret and Dufour, in the presence of feedback control. The system is heated from below and the model used for the nanofluid layer incorporates the effects of thermophoresis and Brownian motion. Three types of bounding systems of the model have been considered which are as follows: both the lower and upper bounding surfaces are free, the lower is rigid and the upper is free, and both of them are rigid. The eigenvalue equations of the perturbed state were obtained from a normal mode analysis and solved using the Galerkin method. It is found that the effect of internal heat source and Soret parameter destabilizes the nanofluid layer system while increasing the Coriolis force, feedback control, and Dufour parameter helps to postpone the onset of convection. Elevating the modified density ratio hastens the instability in the system and there is no significant effect of modified particle density in a nanofluid system. |
| format | Article |
| id | doaj-art-2b42b2878a6c4b3abfc641fdf4b06fbf |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-2b42b2878a6c4b3abfc641fdf4b06fbf2025-08-20T03:54:43ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/27890242789024Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control StrategyI. K. Khalid0N. F. M. Mokhtar1I. Hashim2Z. B. Ibrahim3S. S. A. Gani4Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaSchool of Mathematical Sciences, Faculty of Science and Technology, National University of Malaysia, 43600 Bangi, Selangor, MalaysiaDepartment of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Chemistry, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaA linear stability analysis has been carried out to examine the effect of internal heat source on the onset of Rayleigh–Bénard convection in a rotating nanofluid layer with double diffusive coefficients, namely, Soret and Dufour, in the presence of feedback control. The system is heated from below and the model used for the nanofluid layer incorporates the effects of thermophoresis and Brownian motion. Three types of bounding systems of the model have been considered which are as follows: both the lower and upper bounding surfaces are free, the lower is rigid and the upper is free, and both of them are rigid. The eigenvalue equations of the perturbed state were obtained from a normal mode analysis and solved using the Galerkin method. It is found that the effect of internal heat source and Soret parameter destabilizes the nanofluid layer system while increasing the Coriolis force, feedback control, and Dufour parameter helps to postpone the onset of convection. Elevating the modified density ratio hastens the instability in the system and there is no significant effect of modified particle density in a nanofluid system.http://dx.doi.org/10.1155/2017/2789024 |
| spellingShingle | I. K. Khalid N. F. M. Mokhtar I. Hashim Z. B. Ibrahim S. S. A. Gani Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy Advances in Mathematical Physics |
| title | Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy |
| title_full | Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy |
| title_fullStr | Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy |
| title_full_unstemmed | Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy |
| title_short | Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy |
| title_sort | effect of internal heat source on the onset of double diffusive convection in a rotating nanofluid layer with feedback control strategy |
| url | http://dx.doi.org/10.1155/2017/2789024 |
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