A mathematical model has been constructed for determining the effects of variable viscosity and thermal conductivity on unsteady Jeffery flow over a stretching sheet in the presence of magnetic field and heat generation. The governing partial differential equations are transformed into a set of nonlinear coupled ordinary differential equations and then solved numerically by using the Runge–Kutta–Fehlberg method with shooting technique. A critical analysis with earlier published papers is done and the results are found to be in accordance with each other. Numerical solutions are then obtained and investigated in detail for different physical parameters such as skin-friction coefficient and reduced Nusselt number as well as other parametric values such as the velocity and temperature.

References

References
1.
Erickson
,
L. S.
,
Fan
,
L. T.
, and
Fox
,
V. G.
,
1966
, “
Heat and Mass Transfer on a Moving Continuous Flat Plate With Suction or Injection
,”
Ind. Eng. Chem.
,
5
(
1
), pp.
19
25
.
2.
Tsou
,
F. K.
,
Sparrow
,
E. M.
, and
Goldstein
,
R. J.
,
1967
, “
Flow and Heat Transfer in the Boundary Layer on a Continuous Moving Surface
,”
Int. J. Heat Mass Transfer
,
10
(
2
), pp.
219
235
.
3.
Chakrabarti
,
A.
, and
Gupta
,
A. S.
,
1977
, “
Hydromagnetic Flow and Heat Transfer Over a Stretching Sheet
,”
Q. Appl. Math.
,
37
, pp.
73
78
.
4.
Soundalgekar
,
V. M.
, and
Murty
,
T. V. R.
,
1980
, “
Heat Transfer in MHD Flow With Pressure Gradient, Suction and Injection
,”
J. Eng. Math.
,
14
(
2
), pp.
155
159
.
5.
Chen
,
C. K.
, and
Char
,
M.
,
1988
, “
Heat Transfer of a Continuous Stretching Surface With Suction or Blowing
,”
J. Math. Anal. Applic.
,
135
(
2
), pp.
568
580
.
6.
Kumari
,
M.
, and
Nath
,
G.
,
1999
, “
Flow and Heat Transfer in a Stagnation Point Flow Over a Stretching Sheet With a Magnetic Field
,”
Mech. Res. Commun.
,
26
(
4
), pp.
469
478
.
7.
Vajravelu
,
K.
, and
Rolins
,
D.
,
1992
, “
Heat Transfer in an Electrically Conducting Fluid Over a Stretching Surface
,”
Int. J. Non-Linear Mech.
,
27
(
2
), pp.
265
277
.
8.
Lage
,
J. L.
, and
Bejan
,
A.
,
1990
, “
Convection From a Periodically Stretching Plane Wall
,”
ASME J. Heat Transfer
,
112
(
1
), pp.
92
99
.
9.
Chen
,
C. H.
,
2000
, “
Mixed Convection Cooling of a Heated, Continuously Stretching Surface
,”
Heat Mass Transfer
,
36
(
1
), pp.
79
86
.
10.
Liao
,
S. J.
,
2005
, “
A New Branch of Solutions of Boundary Layer Flows Over an Impermeable Stretched Surface
,”
Int. J. Heat Mass Transfer
,
48
(
12
), pp.
2529
2539
.
11.
Sadeghy
,
K.
,
Najafi
,
A. H.
, and
Saffaripour
,
M.
,
2005
, “
Sakiadis Flow of an Upper-Convected Maxwell Fluid
,”
Int. J. Non-Linear Mech.
,
40
(
9
), pp.
1220
1228
.
12.
Hayat
,
T.
,
Abbas
,
Z.
, and
Sajid
,
M.
,
2006
, “
Series Solution for the Upper-Convected Maxwell Fluid Over a Porous Stretching Plate
,”
Phys. Lett. A
,
358
(5–6), pp.
396
403
.
13.
Hayat
,
T.
,
Abbas
,
Z.
, and
Sajid
,
M.
,
2009
, “
Stagnation-Point Flow of an Upper-Convected Maxwell Fluid Over a Stretching Surface
,”
Chaos, Solitons Fractals
,
39
(
2
), pp.
840
848
.
14.
Abbas
,
Z.
,
Wang
,
Y.
,
Hayat
,
T.
, and
Oberlack
,
M.
,
2010
, “
Mixed Convection in the Stagnation-Point Flow of a Maxwell Fluid Towards a Vertical Stretching Surface
,”
Nonlinear Anal. Real World Appl.
,
11
(
4
), pp.
3218
3228
.
15.
Motsa
,
S. S.
,
Khan
,
Y.
, and
Shatey
,
S.
,
2012
, “
A New Numerical Solution of Maxwell Fluid Over a Shrinking Sheet in the Region of a Stagnation Point
,”
Math. Prob. Eng.
,
2012
, p.
290615
.
16.
Bhattacharyya
,
K.
,
Hayat
,
T.
, and
Gorla
,
R. S. R.
,
2013
, “
Heat Transfer in the Boundary Layer Flow of Maxwell Fluid Over a Permeable Shrinking Sheet
,”
Therm. Energy Power Eng.
,
2
, pp.
72
78
.
17.
Sahoo
,
B.
,
2010
, “
Flow and Heat Transfer of a Non-Newtonian Fluid Past a Stretching Sheet With Partial Slip
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
3
), pp.
602
615
.
18.
Malik
,
M. Y.
,
Zehra
,
I.
, and
Nadeem
,
S.
,
2012
, “
Numerical Treatment of Jeffrey Fluid With Pressure-Dependent Viscosity
,”
Int. J. Numer. Methods Fluids
,
68
(
2
), pp.
196
209
.
19.
Hayat
,
T.
,
Shehzad
,
S. A.
,
Qasim
,
M.
, and
Obaidat
,
S.
,
2012
, “
Radiative Flow of Jeffery Fluid in a Porous Medium With Power Law Heat Flux and Heat Source
,”
Nucl. Eng. Des.
,
243
, pp.
15
19
.
20.
Turkyilmazoglu
,
M.
, and
Pop
,
I.
,
2013
, “
Exact Analytical Solutions for the Flow and Heat Transfer Near the Stagnation Point on a Stretching/Shrinking Sheet in a Jeffrey Fluid
,”
Int. J. Heat Mass Transfer
,
57
(
1
), pp.
82
88
.
21.
Qasim
,
M.
,
2013
, “
Heat and Mass Transfer in a Jeffrey Fluid Over a Stretching Sheet With Heat Source/Sink
,”
Alexandria Eng. J.
,
52
(
4
), pp.
571
575
.
22.
Mustafa
,
M.
,
Hayat
,
T.
, and
Hendi
,
A. A.
,
2012
, “
Influence of Melting Heat Transfer in the Stagnation-Point Flow of a Jeffery Fluid in the Presence of Viscous Dissipation
,”
ASME J. Appl. Mech.
,
79
(
2
), p.
024501
.
23.
Siddheshwar
,
P. G.
, and
Mahabaleswar
,
U. S.
,
2005
, “
Effects of Radiation and Heat Source on MHD Flow of a Viscoelastic Liquid and Heat Transfer Over a Stretching Sheet
,”
Int. J. Non-Linear Mech.
,
40
(
6
), pp.
807
820
.
24.
Ray
,
M. T.
,
Dholey
,
S.
, and
Gupta
,
A. S.
,
2007
, “
Momentum and Heat Transfer in the Magneto-Hydrodynamic Stagnation-Point Flow of a Viscoelastic Fluid Toward a Stretching Surface
,”
Meccanica
,
42
(3), pp.
263
272
.
25.
Mahmoud
,
M. A. A.
,
2010
, “
The Effects of Variable Fluid Properties on MHD Maxwell Fluids Over a Stretching Surface in the Presence of Heat Generation/Absorption
,”
Chem. Eng. Commun.
,
198
(1), pp.
131
146
.
26.
Vajravelu
,
K.
,
Prasad
,
K. V.
, and
Sujatha
,
A.
,
2012
, “
MHD Flow and Mass Transfer of Chemically Reactive Upper Convected Maxwell Fluid Past Porous Surface
,”
Appl. Math. Mech. Engl. Ed.
,
33
(
7
), pp.
899
910
.
27.
Xu
,
L.
, and
Lee
,
E. W. M.
,
2013
, “
Variational Iteration Method for the Magnetohydrodynamic Flow Over a Nonlinear Stretching Sheet
,”
Abstr. Appl. Anal.
,
2013
, pp.
1
5
.
28.
Hayat
,
T.
,
Hussain
,
Q.
, and
Javed
,
T.
,
2009
, “
The Modified Decomposition Method and Pad′e Approximants for the MHD Flow Over A Non-Linear Stretching Sheet
,”
Nonlinear Anal. Real World Appl.
,
10
(
2
), pp.
966
973
.
29.
Gupta
,
P. S.
, and
Gupta
,
A. S.
,
1997
, “
Heat and Mass Transfer on a Stretching Sheet With Suction or Blowing
,”
Can. J. Chem. Eng.
,
55
(6), pp.
744
746
.
30.
Mansur
,
S.
, and
Ishak
,
A.
,
2013
, “
The Flow and Heat Transfer of a Nanofluid Past a Stretching/Shrinking Sheet With a Convective Boundary Condition
,”
Abstr. Appl. Anal.
,
2013
, p.
350647
.
31.
Butt
,
A. S.
, and
Ali
,
S.
,
2014
, “
A Computational Study of Entropy Generation in Magnetohydrodynamic Flow and Heat Transfer Over an Unsteady Stretching Permeable Sheet
,”
Eur. Phys. J. Plus.
,
129
(
13
).
32.
Grubka
,
L. J.
, and
Bobba
,
K. M.
,
1985
, “
Heat Transfer Characteristics of a Continuous, Stretching Surface With Variable Temperature
,”
ASME J. Heat Transfer
,
107
(
1
), pp.
248
250
.
33.
Chen
,
C. H.
,
1988
, “
Laminar Mixed Convection Adjacent to Vertical Continuously Stretching Sheets
,”
Heat Mass Transfer
,
33
(5–6), pp.
471
476
.
34.
Sharma
,
R.
, and
Ishak
,
A.
,
2014
, “
Second Order Slip Flow of Cu-Water Nanofluid Over a Stretching Sheet With Heat Transfer
,”
WSEAS Trans. Fluid Mech.
,
9
, pp.
26
33
.
35.
Dalir
,
N.
,
2014
, “
Numerical Study of Entropy Generation for Forced Convection Flow and Heat Transfer of a Jeffrey Fluid Over a Stretching Sheet
,”
Alexandria Eng. J.
,
53
(
4
) pp.
769
778
.
36.
Pop
,
I.
, and
Na
,
T. Y.
,
1996
, “
Unsteady Flow Past a Stretching Sheet
,”
Mech. Res. Commun.
,
23
(
4
), pp.
413
422
.
37.
Chamkha
,
A. J.
,
1989
, “
Unsteady Hydromagnetic Flow and Heat Isothermal Stretching Sheet Immersed in a Porous Medium
,”
Commun. Heat Mass Transfer
,
25
(6), pp.
899
906
.
38.
Ishak
,
A.
,
2010
, “
Unsteady MHD Flow and Heat Transfer Over a Stretching Plate
,”
J. Appl. Sci.
,
10
(18), pp.
2127
2131
.
39.
Mukhopadhyay
,
S.
,
2011
, “
Heat Transfer Analysis for Unsteady MHD Flow Past a Non-Isothermal Stretching Surface
,”
Nucl. Eng. Des.
,
241
(
12
), pp.
4835
4839
.
40.
Hayat
,
T.
,
Iqbal
,
Z.
,
Mustafa
,
M.
, and
Alsaedi
,
A.
,
2014
, “
Unsteady Flow and Heat Transfer of Jeffrey Fluid Over a Stretching Sheet
,”
Therm. Sci.
,
18
(
4
), pp.
1069
1078
.
41.
Khan
,
Y.
,
Hussain
,
A.
, and
Faraz
,
N.
,
2012
, “
Unsteady Linear Viscoelastic fluid Model Over a Stretching/Shrinking Sheet in the Region of Stagnation Point Flows
,”
Sci. Iran.
,
19
(6), pp.
1541
1549
.
42.
Hayat
,
T.
,
Asad
,
S.
,
Mustafa
,
M.
, and
Alsaedi
,
A.
,
2015
, “
MHD Stagnation-Point Flow of Jeffrey Fluid Over a Convectively Heated Stretching Sheet
,”
Comput. Fluids
,
108
, pp.
179
185
.
43.
Aziz
,
R. C.
,
Hashim
,
I.
, and
Alomari
,
A. K.
,
2011
, “
Thin Film Flow and Heat Transfer on an Unsteady Stretching Sheet With Internal Heating
,”
Mecanica
,
46
(
2
), pp.
349
357
.
44.
Dulal
,
P.
,
2011
, “
Combined Effects of Non-Uniform Heat Source/Sink and Thermal Radiation on Heat Transfer Over an Unsteady Stretching Permeable Surface
,”
Commun. Nonlinear Sci. Numer. Simul.
,
16
(4), pp.
1890
1904
.
45.
Wubshet
,
I. B.
, and
Shanker
,
B.
,
2012
, “
Unsteady MHD Boundary- Layer Flow and Heat Transfer Due to Stretching Sheet in the Presence of Heat Source or Sink
,”
Comput. Fluids
,
70
, pp.
21
28
.
46.
Liu
,
I. C.
, and
Andersson
,
H. I.
,
2008
, “
Heat Transfer in a Liquid Film on an Unsteady Stretching Sheet
,”
Int. J. Therm. Sci.
,
47
(
6
), pp.
766
822
.
47.
Slattery
,
J. C.
,
1972
,
Momentum, Energy and Mass Transfer, in Continua
,
McGraw-Hill
,
New York
.
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