Unsteady couette flow in an annulus with combined mode of magnetic field application: A generalization

Unsteady couette flow in an annulus with combined mode of magnetic field application: A generalization

Michael O. Oni Taiwo S. Yusuf 

Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria

Corresponding Author Email: 
31 December 2017
| Citation



This study generalizes the role of transversely and radially applied magnetic field on flow formation in an annulus. The flow is assumed to be fully developed and driven by the movement of the cylinders. The governing momentum equation is derived and solved using the Laplace transform technique. The impact of moving inner, outer and both cylinders on flow formation is also considered. Result indicate that the application of both magnetic field leads to a further decrease in fluid velocity and an increase in skin-friction at the inner surface of outer cylinder. In addition, the movement of the cylinders is significant in the attainment of steady state skin-friction at the moving wall.


Transverse Magnetic Field, Radial Magnetic Field, Annulus, Unsteady, Couette Flow

1. Introduction
2. Mathematical Analysis
3. Results and Discussions
4. Conclusion

[1] Li Y., Wang D.K., Li Q. (2013). Application of Magneto Hydrodynamics (MHD) in hypersonic vehicle, Advanced Material Research, Vol. 631-632, pp. 890-893.

[2] Rossov V.J. (1957). Flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field, Report 1358 National Advesory Committee for Aeronautics.

[3] Hartmann J. (1937). Hg-Dyanmics I- Theory of laminar flow of an electrically conductive liquid in a homogeneous magnetic field, Kgl. Danske Videnskabernes Salskab, Mathematisk-Fysiske Meddelelser, Vol. 15, No. 6, Copenhagen.

[4] Jha B.K., Odengle J.O. (2015). Unsteady MHD Couette flow in composite channel partially filled with porous material: A semi-analytical approach, Transp Porous Med, Vol. 107, pp. 219 – 234.

[5] Jha B.K., Aina B. (2015). Magnetohydrodynamics of a mixed convection flow in a vertical microannulus: An exact solution, Int. J. Of Fluid Mechanics Research, Vol. 42, No. 6, pp. 537-552. DOI: 10.1615/interJFluidMechRes.V42.16.40

[6] Nandi S. (1973). MHD flow in an annulus with porous walls under an external radial magnetic field, Pageoph, Vol. 105, p. 825.

[7] Jha B.K., Oni M.O. (2017). Impact of mode of application of magnetic field on rate of heat transfer of rarefied gas flow in a microtube, Alexandria Engr. J., DOI: 10.1016/j.aej.2017.03.029

[8] Makinde O.D., Bég O.A., Takhar H.S. (2009). Magnetohydrodynamic viscous flow in a porous medium cylindrical annulus with an applied radial magnetic field, Int J Appl Math Mech, Vol. 5, pp. 68–81.

[9] Katagiri M. (1962). Flow formation in Couette motion in Magnetohydrodynamics, J. Phys. Soc. Jpn. Vol. 17, pp. 393–396.

[10] Jha B.K., Apere C.A. (2013). Time-dependent MHD Couette flow in a porous annulus, Commun. Nonlinear Sci. Numer. Simul, Vol. 18, pp. 1959–1969.

[11] Farhad A., Norzieha M., Sharidan S., Khan I., Samiuthaq Q. (2012). On hydromagnetic rotating flow in a porous medium with slip condition and hall current, Int. J. Phys. Sci., Vol. 7, Vol. 10, pp. 1540–1548.

[12] Pai S.I. (1962). Magnetogasdynamics and plasma dynamics, Springer, Berlin.

[13] Jha B.K., Apere C.A. (2010). Unsteady MHD Couette flow in Annuli: the Riemann-sum approximation, Approach. J. Phy. Soc. Jpn, Vol. 79, No. 12, pp. 124403-124403-5.

[14] Tzou D.Y. (1997). Macro to microscale heat transfer: the lagging behaviour, Taylor and Francis, Washington.