This paper considers the unsteady MHD free convective Couette flow of a viscous incompressible electrically conducting fluid between two parallel vertical porous plates. Both cases of the applied magnetic field being fixed either to the fluid or to the moving porous plate are considered. The solution of the governing equations has been obtained by using a Laplace transform technique. However, the Riemann-sum approximation method is used to invert the Laplace domain to the time domain. The unified solution obtained for the velocity have been used to compute the skin friction, while the temperature has been used to compute the Nusselt number. The effect of various flow parameters entering into the problem such as Prandtl number, Grashof number, and the suction/injection parameter are discussed with the aid of line graphs. The skin friction have been seen to decrease with both suction and injection on the surface of the moving plate when the channel is being cooled, while on the stationary plate, the magnitude of the skin friction increases with injection.
References
1.
Muzychka
, Y. S.
, and Yovanovich
, M. M.
, 2006, “Unsteady Viscous Flows and Stokes’ First Problem
,” Proc. IMECE
, 14301
, pp. 1
–11
.2.
Katagiri
, M.
, 1962, “Flow Formation in Couette Motion in Magnetohydrodynamics
,” J. Phys. Soc. Jpn.
, 17
, pp. 393
–396
.3.
Jana
, R. N.
, Datta
, N.
, and Mazumder
, B. S.
, 1977, “Magnetohydrodynamic Couette Flow and Heat Transfer in a Rotating System
,” J. Phys. Soc. Jpn.
, 42
, pp. 1034
–1039
.4.
Seth
, G. S.
, and Jana
, R. N.
, 1980, “Unsteady Hydromagnetic Flow in a Rotating Channel With Oscillating Pressure Gradient
,” Acta Mech.
, 37
, pp. 29
–34
.5.
Singh
, A. K.
, and Kumar
, N.
, 1983, “Unsteady Hydromagnetic Couette Flow
,” Wear
, 89
, pp. 125
–129
.6.
Mazumder
, B. S.
, 1991, “An Exact Solution of An Oscillatory Couette Flow in a Rotating System
,” Trans. ASME J. Appl. Mech.
, 58
, pp. 1104
–1107
.7.
Ghosh
, S. K.
, 1993, “Unsteady Hydrodynamic Flow in A Rotating Channel With Oscillatory Pressure Gradient
,” J. Phys. Soc. Jpn.
, 62
, pp. 3893
–3905
.8.
Chandran
, P.
, Sacheti
, N. C.
, and Singh
, A. K.
, 1993, “Effect of Rotation on Unsteady Hydromagnetic Couette Flow
,” Astrophys. Space Sci.
, 202
, pp. 1
–10
.9.
Singh
, A. K.
, Sacheti
, N. C.
, and Chandran
, P.
, 1994, “Transient Effects on Magnetohydrodynamics Couette Flow With Rotation: Accelerated Motion
,” Int. J. Eng. Sci.
, 32
, pp. 133
–139
.10.
Guria
, M.
, Jana
, R. N.
, and Ghosh
, S. K.
, 2009, “Oscillatory Couette Flow in the Presence of an Inclined Magnetic Field
,” Meccanica
, 44
, pp. 555
–564
.11.
Das
, S.
, Maji
, S. L.
, Guria
, M.
, and Jana
R. N.,
2009, “Unsteady MHD Couette Flow in a Rotating System
,” Math. Comput. Modell.
, 50
, pp. 1211
–1217
.12.
Nanousis
, N. D.
, Georgantopoulos
, G. A.
, and Papaioannou
, A. I.
, 1980, “Hydromagnetic Free Convection Flow in the Stokes Problem for a Porous Vertical Limiting Surface With Constant Suction
,” Astrophys. Space Sci.
, 70
, pp. 370
–377
.13.
Weir
, A. D.
, 1976, “Axisymmetric Convection in a Rotating Sphere I. Stress-Free Surface
,” J. Fluid Mech.
, 75
, pp. 49
–79
.14.
Soundalgekar
, V. M.
, 1979, “Free Convection Effects on the Flow Past a Vertical Oscillating Plate
,” Astrophys. Space Sci.
, 64
, p. 165172
.15.
Ozoe
, H.
, and Maruo
, E.
, 1987, “Magnetic and Gravitational Natural Convection of Melted Silican: Two-Dimensional Numerical Computations for the Rate of Heat Transfer
,” Jpn. Soc. Mech. Eng.
, 30
, pp. 774
–784
.16.
Georgantopoulos
, G. A.
, Doukas
, C. N.
, Kafousias
, N. G.
, and Goudas
, C. L.
, 1979, “Hydromagnetic Free Convection Effects on the Stokes Problem for an Infinite Vertical Plate
,” Lett. Heat Mass Transfer
, 6
, pp. 397
–404
.17.
Raptis
, A.
, and Singh
, A. K.
, 1983, “MHD Free Convection Flow Past an Accelerated Vertical Plate
,” Int. Commun. Heat Mass Transfer
, 10
, pp. 313
–321
.18.
Singh
, A. K.
, and Singh
, J. N.
, 1989, “Transient MHD Free Convection in a Rotating System
,” Astrophys. Space Sci.
, 162
, pp. 85
–106
.19.
Ferdows
, M.
, Sattar
, M. A.
, and Siddiki
, M. N. A.
, 2004, “Numerical Approach on Parameters of the Thermal Radiation Interaction With Convection in Boundary Layer Flow at a Vertical Plate With Variable Suction
,” Thammasat Int. J. Sci. Tech.
, 9
, pp. 19
–28
.20.
Alam
, M. S.
, Rahman
, M. M.
, and Samad
, M. A.
, 2006, “Dufour and Soret Effects on Unsteady MHD Free Convection and Mass Transfer Flow Past a Vertical Plate in a Porous Medium
,” Nonlinear Anal.: Modell. Control
, 11
, pp. 271
–226
.21.
Singha
, K. G.
, and Deka
, P. N.
, 2006, “Skin-Friction for Unsteady Free Convection MHD Flow Between Two Heated Vertical Parallel Plates
,” Theor. Appl. Mech.
, 33
, pp. 259
–280
.22.
Jha
, B. K.
, 2001, “Natural Convection in Unsteady MHD Couette Flow
,” Heat Mass Transfer
, 37
, pp. 329
–331
.23.
Narahari
, M.
, 2009, “Natural Convection in Unsteady Couette Flow Between Two Vertical Parallel Plates in the Presence of Constant Heat Flux and Radiation
,” Proceedings of the 11th WSEAS International Conference on Mathematics and Computational Methods in Science and Engineering
, pp. 73
–78
.24.
Jha
, B. K.
, and Apere
, C. A.
, 2010, “Unsteady MHD Couette Flow in an Annuli: The Riemann-Sum Approximation to Approach
,” J. Phys. Soc. Jpn.
, 79
, pp. 124403/1
–5
.25.
Khadrawi
, A. F.
, and Al-Nimr
M. A.,
2007, “Unsteady Natural Convection Fluid Flow in a Vertical Microchannel Under the Effect of the Dual-Phase-Lag Heat Conduction Model
,” Int. J. Thermophys.
, 28
, pp. 1387
–1400
.26.
Tzou
, D. Y.
, 1997, “ Macro to Microscale Heat Transfer: The Lagging Behaviour
,” Taylor and Francis
, London.
27.
Narahari
, M.
, 2010, Effect of Thermal Radiation and Free Convection on the Unsteady Couette Flow Between Two Vertical Parallel Plates With Constant Heat Flux at One Boundary
, WSEAS Trans. Heat Mass Transfer
, 5
, pp. 21
–30
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.
