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.

References

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.
You do not currently have access to this content.