Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

doi:10.1007/s10483-014-1868-9

Applied Mathematics and Mechanics (English Edition) ›› 2014, Vol. 35 ›› Issue (10): 1331-1344.doi: https://doi.org/10.1007/s10483-014-1868-9

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

G. S. SETH¹, S. M. HUSSAIN², S. SARKAR¹

1. Department of Applied Mathematics, Indian School of Mines, Dhanbad 826004, India;
2. Department of Mathematics, O. P. Jindal Institute of Technology, Raigarh 496109, India

收稿日期:2013-07-02 修回日期:2014-03-08 出版日期:2014-10-01 发布日期:2014-10-01
通讯作者: G. S. SETH, gsseth_ism@yahoo.com E-mail:gsseth_ism@yahoo.com

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

G. S. SETH¹, S. M. HUSSAIN², S. SARKAR¹

1. Department of Applied Mathematics, Indian School of Mines, Dhanbad 826004, India;
2. Department of Mathematics, O. P. Jindal Institute of Technology, Raigarh 496109, India

Received:2013-07-02 Revised:2014-03-08 Online:2014-10-01 Published:2014-10-01

摘要/Abstract

摘要： This paper presents a study of hydromagnetic Couette flow of an incompressible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymptotic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.

关键词: Ekman number, hydromagnetic Stokes-Ekman boundary layer, magnetic diffusion boundary layer, frequency parameter, magnetic interaction parameter

Abstract: This paper presents a study of hydromagnetic Couette flow of an incompressible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymptotic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.

Key words: magnetic diffusion boundary layer, Ekman number, magnetic interaction parameter, frequency parameter, hydromagnetic Stokes-Ekman boundary layer

中图分类号:

O357.1

G. S. SETH;S. M. HUSSAIN;S. SARKAR. Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(10): 1331-1344.

参考文献

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[19] Benton, E. R. and Loper, D. E. On the spin-up of an electrically conducting fluid, part 1, the unsteady hydromagnetic Ekman-Hartman boundary layer problem. Journal of Fluid Mechanics, 39, 561-586 (1969)

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

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