Bifurcation phenomena and control for magnetohydrodynamic flows in a smooth expanded channel

doi:10.1088/1674-1056/23/11/114701

›› 2014, Vol. 23 ›› Issue (11): 114701-114701.doi: 10.1088/1674-1056/23/11/114701

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Bifurcation phenomena and control for magnetohydrodynamic flows in a smooth expanded channel

G. C. Layek^a, Mani Shankar Mandal^b, H. A. Khalaf^c

a Department of Mathematics, The University of Burdwan, Burdwan 713104, India;
b Department of Mathematics, Krishnagar Govt. College, Krishnagar, Nadia 741101, India;
c Thi-Qar University, Marshes Research Center, Thi-Qar, Iraq

收稿日期:2014-01-16 修回日期:2014-04-17 出版日期:2014-11-15 发布日期:2014-11-15
基金资助:
Project support by the UGC (SAP), DSA-I in the Mathematics Department, Burdwan University, India.

Bifurcation phenomena and control for magnetohydrodynamic flows in a smooth expanded channel

G. C. Layek^a, Mani Shankar Mandal^b, H. A. Khalaf^c

a Department of Mathematics, The University of Burdwan, Burdwan 713104, India;
b Department of Mathematics, Krishnagar Govt. College, Krishnagar, Nadia 741101, India;
c Thi-Qar University, Marshes Research Center, Thi-Qar, Iraq

Received:2014-01-16 Revised:2014-04-17 Online:2014-11-15 Published:2014-11-15
Contact: Mani Shankar Mandal E-mail:manimath@yahoo.com
Supported by:
Project support by the UGC (SAP), DSA-I in the Mathematics Department, Burdwan University, India.

摘要/Abstract

摘要： This work reports the effects of magnetic field on an electrically conducting fluid with low electrical conductivity flowing in a smooth expanded channel. The governing nonlinear magnetohydrodynamic (MHD) equations in induction-free situations are derived in the framework of MHD approximations and solved numerically using the finite-difference technique. The critical values of Reynolds number (based on upstream mean velocity and channel height) for symmetry breaking bifurcation for a sudden expansion channel (1:4) is about 36, whereas the value in the case of the smooth expansion geometry used in this work is obtained as 298, approximately (non-magnetic case). The flow of an electrically conducting fluid in the presence of an externally applied constant magnetic field perpendicular to the plane of the flow is reduced significantly depending on the magnetic parameter (M). It is found that the critical value of Reynolds number for smooth expansion (1:4) is about 475 for the magnetic parameter M=2. The separating regions developed behind the smooth symmetric expansion are decreased in length for increasing values of the magnetic parameter. The bifurcation diagram is shown for a symmetric smoothly expanding channel. It is noted that the critical values of Reynolds number increase with increasing magnetic field strength.

关键词: weakly electrically conducting fluid, flow bifurcation, asymmetric flow, smooth expansion

Abstract: This work reports the effects of magnetic field on an electrically conducting fluid with low electrical conductivity flowing in a smooth expanded channel. The governing nonlinear magnetohydrodynamic (MHD) equations in induction-free situations are derived in the framework of MHD approximations and solved numerically using the finite-difference technique. The critical values of Reynolds number (based on upstream mean velocity and channel height) for symmetry breaking bifurcation for a sudden expansion channel (1:4) is about 36, whereas the value in the case of the smooth expansion geometry used in this work is obtained as 298, approximately (non-magnetic case). The flow of an electrically conducting fluid in the presence of an externally applied constant magnetic field perpendicular to the plane of the flow is reduced significantly depending on the magnetic parameter (M). It is found that the critical value of Reynolds number for smooth expansion (1:4) is about 475 for the magnetic parameter M=2. The separating regions developed behind the smooth symmetric expansion are decreased in length for increasing values of the magnetic parameter. The bifurcation diagram is shown for a symmetric smoothly expanding channel. It is noted that the critical values of Reynolds number increase with increasing magnetic field strength.

Key words: weakly electrically conducting fluid, flow bifurcation, asymmetric flow, smooth expansion

中图分类号: (Laminar flows)

47.15.-x

47.85.L- (Flow control) 47.85.-g (Applied fluid mechanics)

G. C. Layek, Mani Shankar Mandal, H. A. Khalaf. Bifurcation phenomena and control for magnetohydrodynamic flows in a smooth expanded channel[J]. , 2014, 23(11): 114701-114701.

G. C. Layek, Mani Shankar Mandal, H. A. Khalaf. Bifurcation phenomena and control for magnetohydrodynamic flows in a smooth expanded channel[J]. Chin. Phys. B, 2014, 23(11): 114701-114701.

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Bifurcation phenomena and control for magnetohydrodynamic flows in a smooth expanded channel

Bifurcation phenomena and control for magnetohydrodynamic flows in a smooth expanded channel

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