### Abstract

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.

Original language | English |
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Article number | 2789024 |

Journal | Advances in Mathematical Physics |

Volume | 2017 |

DOIs | |

Publication status | Published - 2017 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Applied Mathematics

### Cite this

*Advances in Mathematical Physics*,

*2017*, [2789024]. https://doi.org/10.1155/2017/2789024

**Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy.** / Khalid, I. K.; Mokhtar, N. F.M.; Hashim, Ishak; Ibrahim, Z. B.; Gani, S. S.A.

Research output: Contribution to journal › Article

*Advances in Mathematical Physics*, vol. 2017, 2789024. https://doi.org/10.1155/2017/2789024

}

TY - JOUR

T1 - Effect of Internal Heat Source on the Onset of Double-Diffusive Convection in a Rotating Nanofluid Layer with Feedback Control Strategy

AU - Khalid, I. K.

AU - Mokhtar, N. F.M.

AU - Hashim, Ishak

AU - Ibrahim, Z. B.

AU - Gani, S. S.A.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85026531405&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85026531405&partnerID=8YFLogxK

U2 - 10.1155/2017/2789024

DO - 10.1155/2017/2789024

M3 - Article

AN - SCOPUS:85026531405

VL - 2017

JO - Advances in Mathematical Physics

JF - Advances in Mathematical Physics

SN - 1687-9120

M1 - 2789024

ER -