**6. References**

206 Topics in Magnetohydrodynamics

linear distribution; thus, the shearing can unattenuately extend to the whole flow domain from the boundaries, corresponding to a shear-thickening phenomenon. A further increase

behaviour depends strongly on the choice of the parameters, for example, for large *H* , *u*

will not effect this velocity component further. The magnitude of velocity component


(a) (b)

The unsteady rotating flow of a uniformly conducting incompressible fourth-grade fluid between two parallel infinite plates in the presence of a magnetic field is modeled. The steady rotating flow of the non-Newtonian fluid subject to a uniform transverse magnetic field is studied. The governing non-linear equations are solved numerically. The numerical results of the non-Newtonian fluid are compared with those of a Newtonian fluid. The

The transverse magnetic field decelerates the fluid motion. When the strength of the

 It is observed that the boundary layer thickness decreases drastically by increasing . *H* It means that the magnetic field provides some mechanism to control the boundary

Fig. 4. Variation of velocity components *u* and *v* with *z* for large values of

major findings of the present works can be summarized as follows:

magnetic field increases, the flow velocity decreases.





**v**




0

for small . *H* On the contrary, the magnitude of velocity component *v*

increases and the curvature of the velocity profile decreases with an

(see Figs. 3c, 3d and 4b). It is also found that the flow

, whereas this velocity component is

0 0.5 1

Effect of material parameter

**z**

H = 5 E = 1

β = 1 β = 5 β = 10 β = 15 β = 20

of 

*v* decreases when

independent of

decreases with

0

**5. Conclusions** 

layer thickness.

0.2

0.4

0.6

**u**

0.8

1

1.2

increases with an increase of material parameter

Effect of material parameter

0 0.5 1 **z**

1,5, 10, 15,20; fixing 1, 5 *E H* .

H = 5 E = 1

for both small and large values of . *H*

increase in material parameter

β = 1 β = 5 β = 10 β = 15 β = 20


[40] M. Turkylimazoglu, Unsteady MHD flow with variable viscosity: Applications of

[41] T. Hayat, C. Fetecaua, M. Sajid, Analytic solution for MHD Transient rotating flow of a

[44] A.C. Eringen, Theory of thermomicropolar fluids, Math. Anal. Appl. 38 (1972) 480– 496. [45] N.T. Eldabe, E.F. Elshehawey, Elsayed M.E. Elbarbary, Nasser S. Elgazery, Chebyshev

[47] M.I. Char, Heat and mass transfer in a hydromagnetic flow of viscoelastic fluid over a

[48] A. Raptis, Flow of a micropolar fluid past a continuously moving plate by the presence

[49] A. Raptis, C. Perdikis, Viscoelastic flow by the presence of radiation. ZAMM 78 (1998)

[50] A. Raptis, C. Pardikis, H.S. Takhar, Effect of thermal radiation on MHD flow, Appl.

[51] P. G. Siddheshwar, U.S. Mahabaleswar, Effects of radiation and heat source on MHD

[52] S.K. Khan, Heat transfer in a viscoelastic fluid flow over a stretching surface with heat

[53] M.S. Abel, P.G. Siddheshwar, M. Nandeppanavar Mahantesh, Heat transfer in a

and non-uniform heat source, Int. J. Heat Mass Transfer 50 (2007) 960–966. [54] M.S. Abel, M.M. Nandeppanavar, Heat transfer in MHD viscoelastic boundary layer

[55] M.M. Nandeppanavar, M.S. Abel, J. Tawade, Heat transfer in a Walter's liquid B

[56] M. Mahantesh, Nandeppanavar, K. Vajravelu, M. Subhas Abel, Heat transfer in MHD

[57] Kayvan Sadeghy, Navid Khabazi, Seyed-Mohammad Taghavi, Magnetohydrodynamic

flow of a visco-elastic liquid and heat transfer over a stretching sheet, Int. J. Non-

source/sink, suction/blowing and radiation, Int. J. Heat Mass transfer 49 (2006)

viscoelastic boundary layer flow over a stretching sheet with viscous dissipation

flow over a stretching sheet with non-uniform heat source/sink, Commun.

fluid over an impermeable stretching sheet with non-uniform heat source/sink and elastic deformation, Commun. Nonlinear Sci. Numer. Simul. 15 (2010) 1791–

viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink, Commun. Nonlinear Sci. Numer. Simulat. 16 (2011)

(MHD) flows of viscoelastic fluids in converging/diverging Channels, Int. J.

second grade fluid in a porous space, Nonlinear Analysis: Real World Applications

finite difference method for MHD flow of a micropolar fluid past a stretching sheet with heat transfer, Applied Mathematics and Computation 160 (2005) 437–450. [46] T. Sarpakaya, Flow of non-Newtonian fluids in magnetic field, AIChE J 7 (1961) 324–

spectral scheme, Int. J. Thermal Sci. 49 (2010) 563-570.

[42] A.C. Eringen, Simple microfluids, Int. J. Eng. Sci. 2 (1964) 203–217. [43] A.C. Eringen, Theory of micropolar fluids, Math. Mech. 16 (1966) 1–18.

stretching sheet, J. Math. Annal Appl. 186 (1994) 674–689.

of radiation, Int. J. Heat Mass transfer 41 (1998) 2865–2866.

Nonlinear Sci. Numer. Simul. 14 (2009) 2120–2131.

Math. Comput. 153 (2004) 645–649.

linear Mech. 40 (2005) 807–821.

9 (2008) 1619 – 1627.

328.

277–279.

628–639.

1802.

3578–3590.

Engng. Sci. 45 (2007) 923–938.


208 Topics in Magnetohydrodynamics

[21] A.M. Sidiqui, M.A. Rana, Naseer Ahmed, Magnetohydrodynamic flow of a Burgers'

[22] A.M. Sidiqui, M.A. Rana, Naseer Ahmed, Hall effects on flow and heat transfer in the hydromagnetic Burgers Ekman layer, Int. J. Moder. Math. 2(2) (2007) 255-268. [23] S.R. Kasiviswanathan and A.R. Rao, On exact solutions of unsteady MHD flow between eccentrically rotating disks, Arch, Mech., 39(4) (1987) 411-418. [24] H.K. Mohanty, Hydromagnetic flow between two rotating disk with non-coincident

[26] S.N. Murthy, R.K.P. Ram, MHD flow and heat transfer due to eccentric rotation of a porous disk and a fluid at infinity, Int. J. Engng. Sci. 16(1978) 943-949. [27] P.N. Kaloni and A.M. Siddiqui, A note on the flow of viscoelastic fluid between

[28] A.M. Siddiqui, T. Haroon and S. Asghar, Unsteady MHD flow of non-Newtonian fluid

[29] A.M. Sidiqui, M.A. Rana, Naseer Ahmed, Effects of Hall current and heat transfer on

[30] G. Palani, I.A. Abbas, Free Convection MHD Flow with Thermal Radiation from an

[31] M. Farzaneh-Gord, A. A. Joneidi, and B. Haghighi, Investigating the effects of the

[32] E.R. Maki, D .Kuzma, R.L. Donnelly, B. Kim, Magnetohydrodynamic lubrication flow

[33] W.F. Hughes, R.A. Elco, Magnetohydrodynamic lubrication flow between parallel

[34] D.C. Kuzma, E.R. Maki, R.J. Donnelly, The magnetohydrodynamic squeeze film, J.

[35] E.A. Hamza, The magnetohydrodynamic squeeze film, J. Fluid Mech. 19 (1964) 395–

[36] E.A. Hamza, The magnetohydrodynamic effects on a fluid film squeezed between two

[37] S. Bhattacharyya, A. Pal, Unsteady MHD squeezing flow between two parallel rotating

[38] Erik Sweet, K. Vajravelu, A. Robert. Van Gorder, I. Pop, Analytical solution for the

[39] Z. Abbas, T. Javed, M. Sajid, N. Ali, Unsteady MHD flow and heat transfer on a

unsteady MHD flow of a viscous fluid between moving parallel plates, Commun.

stretching sheet in a rotating fluid, Journal of the Taiwan Institute of Chemical

due to eccentric rotations of a porous disk and a fluid at infinity, Acta Mech. 147

MHD flow of a Burgers' fluid due to a pull of eccentric rotating disks, Commun.

Impulsively-Started Vertical Plate, Nonlinear Analysis: Modelling and Control,

important parameters on magnetohydrodynamics flow and heat transfer over a stretching sheet, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 2010 224:

eccentric disks, J. Non-Newtonian Fluid Mech. 26 (1987). 125–133.

parallel axes of rotation, Phys., Fluids 15 (1972) 1456-1458.

Nonlinear Sci. Numer. Simul. 13(2008) 1554-1570.

between parallel plates. J. Fluid Mech. 26 (1966) 537–543.

rotating surfaces, J. Phys. D: Appl. Phys. 24 (1991) 547–554.

rotating disks. J. Fluid Mech. 13 (1962) 21–32.

discs, Mech. Res. Commun. 24 (1997) 615–623.

Nonlinear Sci. Numer. Simulat. 16 (2011) 266–273.

[25] C.S. Erkman, Lett. Appl. Engng. Sci. 3(1975) 51.

2892.

(2000), 99-109.

14(1) (2009) 73–84.

1DOI:10.1243/09544089JPME258.

Tribol 110 (1988) 375–377.

Engineers 41 (2010) 644–650.

400.

fluid in an orthogonal rheometer, Applied Mathematical Modelling, 34(2010) 2881-


210 Topics in Magnetohydrodynamics

[58] B. D. Coleman and W. Noll, An approximation theorem for functionals with

[59] K.A Hoffmann, S. Chiang, Computational fluid dynamics for engineers, I, 1995, P.

370.

92.

applications continuum mechanics, Arch. Rational Mech. Anal. 6 (1960) 355-
