The steady hydromagnetic flow of a viscous, incompressible, perfectly conducting, and heat absorbing fluid past a vertical flat plate under the influence of an aligned magnetic field is studied. The flow is subject to mixed convective heat transfer. The fluid is assumed to have a reasonably high magnetic Prandtl number which causes significant-induced magnetic field effects. Such fluid flows find application in many magnetohydrodynamic devices including MHD power-generation. The effects of viscous dissipation and heat absorption by the fluid are investigated. The governing nonlinear partial differential equations are converted into a set of nonsimilar partial differential equations which are then solved using a spectral quasi-linearization method (SQLM). The effects of the important parameters on the fluid velocity, induced magnetic field, fluid temperature and as well as on the coefficient of skin-friction and the Nusselt number are discussed qualitatively.
Issue Section:
Research Papers
References
1.
Ching-Lai
, H.
, Knieper
, P. J.
, and Liang-Tseng
, F.
, 1966
, “Heat Transfer to MHD Flow in the Thermal Entrance Region of a Flat Duct
,” Int. J. Heat Mass Transfer
, 9
(8
), pp. 773
–789
.2.
LalithaRamamoorthy
, P.
, 1968
, “Solutions of MHD Boundary Layer Equations With Transverse Magnetic Field and Arbitrary Pressure Gradient
,” Proc. Indian Acad. Sci. A
, 68
(5
), pp. 251
–264
.3.
Tan
, C. W.
, 1970
, “Low Speed MHD Couette Flow of a Slightly Rarefied and Electrically Conducting Gas
,” Appl. Sci. Res.
, 22
(1
), pp. 201
–222
.4.
Reznikov
, B. I.
, and Smyslov
, Y. N.
, 1971
, “MHD Flow in the Vicinity of the Stagnation Point in a Purely Azimuthal Magnetic Field
,” Fluid Dyn.
, 2
(4
), pp. 1
–4
.5.
Chuang
, H.
, 1972
, “Effects of Transpiration on the MHD Flow Near an Oscillating Plate
,” Int. J. Heat Mass Transfer
, 15
(3
), pp. 563
–566
.6.
Rav
, V. V. R.
, and Sithapathi
, A.
, 1973
, “On MHD Flow Along an Infinite Wall With Constant Suction
,” Proc. Indian Acad. Sci. A
, 77
(1
), pp. 42
–50
.7.
Suwa
, S.
, 1973
, “Magnetohydrodynamical Steady Aligned Flow Past an Oblique Flat Plate at a High Reynolds Number
,” J. Phys. Soc. Jpn.
, 34
(6
), pp. 1649
–1658
.8.
Lakin
, W. D.
, 1974
, “Magnetohydrodynamic Flow Past a Finite Flat Plate in the Presence of a Nonaligned Magnetic Field
,” Can. J. Phys.
, 52
(12
), pp. 1104
–1106
.9.
Aldoss
, T. K.
, Al-Nimr
, M. A.
, Jarrah
, M. A.
, and Al-Shaer
, B. J.
, 1995
, “Magnetohydrodynamic Mixed Convection From a Vertical Plate Embedded in a Porous Medium
,” Numer. Heat Transfer
, 28
(5
), pp. 635
–645
.10.
Aldoss
, T. K.
, 1996
, “MHD Mixed Convection From a Vertical Cylinder Embedded in a Porous Medium
,” Int. Commun. Heat Mass Transfer
, 23
(4
), pp. 517
–530
.11.
Chamkha
, A. J.
, 1997
, “MHD-Free Convection From a Vertical Plate Embedded in a Thermally Stratified Porous Medium With Hall Effects
,” Appl. Math. Model
, 21
(10
), pp. 603
–609
.12.
Chamkha
, A. J.
, 2001
, “Coupled Heat and Mass Transfer by Natural Convection About a Truncated Cone in the Presence of Magnetic Field and Radiation Effects
,” Numer. Heat Transfer A
, 39
(5
), pp. 511
–530
.13.
Azzam
, G. E. A.
, 2002
, “Radiation Effects on the MHD Mixed Free-Forced Convective Flow Past a Semi-Infinite Moving Vertical Plate for High Temperature Differences
,” Phys. Scr.
, 66
(1
), pp. 71
–76
.14.
Duwairi
, H. M.
, and Damesh
, R. A.
, 2004
, “MHD-Buoyancy Aiding and Opposing Flows With Viscous Dissipation Effects From Radiate Vertical Surfaces
,” Can. J. Chem. Eng.
, 82
(3
), pp. 613
–618
.15.
Chamkha
, A. J.
, Takhar
, H. S.
, and Nath
, G.
, 2004
, “Mixed Convection Flow Over a Vertical Plate With Localized Heating (Cooling), Magnetic Field and Suction (Injection)
,” Heat Mass Transfer
, 40
(11
), pp. 835
–841
.16.
Sharma
, P. R.
, and Yadav
, G. R.
, 2007
, “Unsteady MHD Forced and Free Convection Three-Dimensional Flow Heat and Mass Transfer Along an Infinite Vertical Porous Plate With Periodic Suction
,” Modell. Meas. Control B
, 76
(1–2
), pp. 11
–33
.17.
Abdelkhalek
, M. M.
, 2006
, “The Skin Friction in the MHD Mixed Convection Stagnation Point With Mass Transfer
,” Int. Commun. Heat Mass Transfer
, 33
(2
), pp. 249
–258
.18.
Ishak
, A.
, Nazar
, R.
, Arifin
, N. M.
, and Pop
, I.
, 2007
, “Dual Solutions in Magnetohydrodynamic Mixed Convection Flow Near a Stagnation-Point on a Vertical Surface
,” ASME J. Heat Transfer
, 129
(9
), pp. 1212
–1216
.19.
Makinde
, O. D.
, and Sibanda
, P.
, 2008
, “Magnetohydrodynamic Mixed Convective Flow and Heat and Mass Transfer Past a Vertical Plate in a Porous Medium With Constant Wall Suction
,” ASME J. Heat Transfer
, 130
(11
), p. 11260
.20.
Aydin
, O.
, and Kaya
, A.
, 2008
, “Radiation Effect on MHD Mixed Convection Flow About a Permeable Vertical Plate
,” Heat Mass Transfer
, 45
(2
), pp. 239
–246
.21.
Ishak
, A.
, Nazar
, R.
, and Pop
, I.
, 2009
, “MHD Convective Flow Adjacent to a Vertical Surface With Prescribed Wall Heat Flux
,” Int. Commun. Heat Mass Transfer
, 36
(6
), pp. 554
–557
.22.
Takhar
, H. S.
, Roy
, S.
, and Nath
, G.
, 2003
, “Unsteady Free Convection Flow of an Infinite Vertical Porous Plate Due to the Combined Effects of Thermal and Mass Diffusion, Magnetic Field and Hall Currents
,” Heat Mass Transfer
, 39
(10
), pp. 825
–834
.23.
Ishak
, A.
, Nazar
, R.
, Bachok
, N.
, and Pop
, I.
, 2010
, “MHD Mixed Convection Flow Near the Stagnation-Point on a Vertical Permeable Surface
,” Phys. A: Stat. Mech. Appl.
, 389
(1
), pp. 40
–46
.24.
Kumari
, M.
, and Nath
, G.
, 2010
, “Unsteady MHD Mixed Convection Flow Over an Impulsively Stretched Permeable Vertical Surface in a Quiescent Fluid
,” Int. J. Nonlinear Mech.
, 45
(3
), pp. 310
–319
.25.
Ali
, F. M.
, Nazar
, R.
, Arifin
, N. M.
, and Pop
, I.
, 2011
, “Effect of Hall Current on MHD Mixed Convection Boundary Layer Flow Over a Stretched Vertical Flat Plate
,” Meccanica
, 46
(5
), pp. 1103
–1112
.26.
Chamkha
, A. J.
, Mohamed
, R. A.
, and Ahmed
, S. E.
, 2011
, “Unsteady MHD Natural Convection From a Heated Vertical Porous Plate in a Micropolar Fluid With Joule Heating, Chemical Reaction and Radiation Effects
,” Meccanica
, 46
(2
), pp. 399
–411
.27.
Vajravelu
, K.
, and Nayfeh
, J.
, 1992
, “Hydromagnetic Convection at a Cone and a Wedge
,” Int. Commun. Heat Mass Transfer
, 19
(5
), pp. 701
–710
.28.
Vajravelu
, K.
, and Hadjinicolaou
, A.
, 1993
, “Heat Transfer in a Viscous Fluid Over a Stretched Sheet With Viscous Dissipation and Internal Heat Generation
,” Int. Commun. Heat Mass Transfer
, 20
(3
), pp. 417
–430
.29.
Chamkha
, A. J.
, and Khaled
, A. R. A.
, 2000
, “Hydromagnetic Combined Heat and Mass Transfer by Natural Convection From a Permeable Surface Embedded in a Fluid Satural Porous Medium
,” Int. J. Numer. Methods Heat Fluid Flow
, 10
(5
), pp. 455
–476
.30.
Chamkha
, A. J.
, 2003
, “MHD Flow of a Uniformly Stretched Vertical Permeable Surface in the Presence of Heat Generation/Absorption and a Chemical Reaction
,” Int. Commun. Heat Mass Transfer
, 30
(3
), pp. 413
–422
.31.
Al-Mudhaf
, A.
, and Chamkha
, A. J.
, 2005
, “Similarity Solutions for MHD Thermosolutal Marangoni Convection Over a Flat Surface in the Presence of Heat Generation or Absorption Effects
,” Heat Mass Transfer
, 42
(2
), pp. 112
–121
.32.
Chamkha
, A. J.
, and Al-Mudhaf
, A.
, 2005
, “Unsteady Heat and Mass Transfer From a Rotating Vertical Cone With a Magnetic Field and Heat Generation or Absorption Effects
,” Int. J. Therm. Sci.
, 44
(3
), pp. 267
–276
.33.
Mahmoud
, M.
, and Waheed
, S.
, 2010
, “Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid Over a Heated Stretching Surface
,” Math. Probl. Eng.
, 2010
, p. 579162
.34.
Chamkha
, A. J.
, and Ahmed
, S. E.
, 2011
, “Similarity Solution for Unsteady MHD Flow Near a Stagnation Point of a Three-Dimensional Porous Body With Heat and Mass Transfer, Heat Generation/Absorption and Chemical Reaction
,” J. Appl. Fluid Mech.
, 4
(6
), pp. 87
–94
.35.
Makinde
, O. D.
, 2012
, “Heat and Mass Transfer by MHD Mixed Convection Stagnation Point Flow Toward a Vertical Plate Embedded in a Highly Porous Medium With Radiation and Internal Heat Generation
,” Meccanica
, 47
(5
), pp. 1173
–1184
.36.
Mishra
, U.
, and Singh
, G.
, 2014
, “MHD Mixed Convection and Mass Transfer Due to Unsteady Stretching Sheet
,” Heat Transfer Asian Res.
, 43
(5
), pp. 447
–458
.37.
Afzal
, N.
, 1972
, “Heat Transfer in MHD Flow With Aligned Field on a Flat Plate at High Prandtl Number
,” Int. J. Heat Mass Transfer
, 15
(4
), pp. 863
–865
.38.
Takhar
, H. S.
, Chamkha
, A. J.
, and Nath
, G.
, 1999
, “Unsteady Flow and Heat Transfer on a Semi-Infinite Flat Plate With an Aligned Magnetic Field
,” Int. J. Eng. Sci.
, 37
(13
), pp. 1723
–1736
.39.
Zueco
, J.
, and Ahmed
, S.
, 2010
, “Combined Heat and Mass Transfer by Mixed Convection MHD Flow Along a Porous Plate With Chemical Reaction in Presence of Heat Source
,” Appl. Math. Mech.
, 31
(10
), pp. 1217
–1230
.40.
Haque
, M. M.
, and Alam
, M. M.
, 2009
, “Transient Heat and Mass Transfer by Mixed Convection Flow From a Vertical Porous Plate With Induced Magnetic Field, Constant Heat and Mass Fluxes
,” Modell. Meas. Control B
, 78
(3–4
), pp. 54
–73
.41.
Ali
, F. M.
, Nazar
, R.
, Arifin
, N. M.
, and Pop
, I.
, 2011
, “MHD Mixed Convection Boundary Layer Flow Toward a Stagnation Point on a Vertical Surface With Induced Magnetic Field
,” ASME J. Heat Transfer
, 133
(2
), p. 022502
.42.
Ahmed
, N.
, and Kalita
, H.
, 2015
, “Similarity Solution to Hydrodmagnetic Flow Past a Continuously Moving Semi-Infinite Vertical Porous Plate With Large Suction
,” Heat Transfer Asian Res.
, 44
(1
), pp. 66
–87.
43.
Cramer
, K.
, and Pai
, S.
, 1973
, Magnetofluiddynamics for Engineers and Applied Physicists
, McGraw-Hill Book Company
, New York
.44.
Kumar
, A.
, and Singh
, A. K.
, 2013
, “Unsteady MHD Free Convective Flow past a Semi-Infinite Vertical Wall With Induced Magnetic Field
,” Appl. Math. Comput.
, 222
, pp. 462
–471
.45.
Bellman
, R. E.
, and Kalaba
, R. E.
, 1965
, Quasilinearization and Nonlinear Boundary-Value Problems
, Elsevier
, New York
.46.
Trefethen
, L. N.
, 2000
, Spectral Methods in Matlab
, SIAM
, Philadelphia, PA.Copyright © 2018 by ASME
You do not currently have access to this content.
