Unsteady flow of a third grade fluid in the presence of Soret and Dufour effects is considered. Employing similarity transformations, the governing equation for the velocity, concentration, and temperature fields is presented. The computations for the corresponding problems are performed by using a homotopy analysis method (HAM). The associated behavior of the flow parameters is discussed and important conclusions have been pointed out.

References

1.
Tan
,
W. C.
, and
Xu
,
M. Y.
, 2002, “
Plane Surface Suddenly Set in Motion in a Viscoelastic Fluid With Fractional Maxwell Model
,”
Acta Mech. Sin.
,
18
(
4
), pp.
342
349
.
2.
Tan
,
W. C.
,
Pan
,
W.
, and
Xu
,
M.
, 2003, “
A Note on Unsteady Flows of a Viscoelastic Fluid With the Fractional Maxwell Model Between Two Parallel Plates
,”
Int. J. Non-Linear Mech.
,
38
(
5
), pp.
645
650
.
3.
Tan
,
W. C.
, and
Masuoka
,
T.
, 2005, “
Stokes First Problem for a Second Grade Fluid in a Porous Half Space With Heated Boundary
,”
Int. J. Non-Linear Mech.
,
40
(
4
), pp.
515
522
.
4.
Fetecau
,
C.
, and
Fetecau
,
C.
, 2006, “
Starting Solutions for the Motion of a Second Grade Fluid due to Longitudinal and Torsional Oscillations of a Circular Cylinder
,”
Int. J. Eng. Sci.
,
44
(
11-12
), pp.
788
796
.
5.
Fetecau
,
C.
,
Fetecau
,
C.
, and
Vieru
,
D.
, 2007, “
On Some Helical Flows of Oldroyd-B Fluids
,”
Acta Mech.
,
189
(
1-4
), pp.
53
63
.
6.
Fetecau
,
C.
,
Prasad
,
S. C.
, and
Rajagopal
,
K. R.
, 2007, “
A Note on the Flow Induced by a Constantly Accelerating Plate in an Oldroyd-B Fluid
”,
Appl. Math. Model.
,
31
(
4
), pp.
647
654
.
7.
Vieru
,
D.
,
Fetecau
,
C.
, and
Fetecau
,
C.
, 2008, “
Flow of a Viscoelastic Fluid With Fractional Maxwell Model Between Two Side Walls Perpendicular to a Plate
,”
Appl. Math. Comput.
,
200
(
1
), pp.
459
464
.
8.
Cortell
,
R.
, 2006, “
Effects of Viscous Dissipation and Work Done by Deformation on the MHD Flow and Heat Transfer of a Viscoelastic Fluids Over a Stretching Sheet
,”
Phys. Lett. A
,
357
(
4-5
), pp.
298
305
.
9.
Kothandapani
,
M.
, and
Srinivas
,
S.
, 2008, “
Peristaltic Transport of a Jeffrey Fluid Under the Effect of Magnetic Field in an Asymmetric Channel
,”
Int. J. Non-Linear Mech.
,
43
(
9
), pp.
915
924
.
10.
Hayat
,
T.
,
Awais
,
M.
, and
Sajid
,
M.
, 2011, “
Mass Transfer Effects on the Unsteady Flow of UCM Fluid Over a Stretching Sheet
,”
Int. J. Mod. Phys. B
,
25
(
21
), pp.
2863
2878
.
11.
Mollica
,
F.
, and
Rajagopal
,
K. R.
, 1999, “
Secondary Flows due to Axial Shearing of a Third-Grade Fluid Between Two Eccentrically Placed Cylinders
,”
Int. J. Eng. Sci.
,
37
(
4
), pp.
411
429
.
12.
Fosdick
,
R. L.
, and
Rajagopal
,
K. R.
, 1980, “
Thermodynamics and Stability of Fluids of Third Grade
,”
Proc. R. Soc. London, Ser. A
,
339
(
1738
), pp.
351
377
.
13.
Hayat
,
T.
,
Nadeem
,
S.
,
Asghar
,
S.
, and
Siddiqui
,
A. M.
, 2001, “
MHD Rotating Flow of a Third Grade Fluid on an Oscillating Plate
,”
Acta Mech.
,
152
(
1-4
), pp.
177
190
.
14.
Iqbal
,
S.
,
Ansari
,
A. R.
,
Siddiqui
,
A. M.
, and
Javed
,
A.
, 2011, “
Use of Optimal Homotopy Asymptotic Method and Galerkin’s Finite Element Formulation in the Study of Heat Transfer Flow of a Third Grade Fluid Between Parallel Plates
,”
ASME J. Heat Transfer
,
133
(
9
),
091702
.
15.
Hayat
,
T.
,
Iqbal
,
Z.
,
Mustafa
,
M.
, and
Hendi
,
A. A.
, 2011, “
Melting Heat Transfer in the Stagnation Point Flow of Third-Grade Fluid Past a Stretching Sheet With Viscous Dissipation
,”
Therm. Sci.
16.
Eckert
,
E. R. G.
, and
Drake
,
R. M.
, 1972,
Analysis of Heat and Mass Transfer
,
McGraw-Hill
,
New York
.
17.
Mansour
,
M. A.
,
Anssary
,
N. F. E.
, and
Aly
,
A. M.
, 2008, “
Effects of Chemical Reaction and Thermal Stratification on MHD Free Convective Heat and Mass Transfer Over a Vertical Stretching Surface Embedded in a Porous Media Considering Soret and Dufour Numbers
,”
Chem. Eng. J.
,
145
(
2
), pp.
340
345
.
18.
Tsai
,
R.
, and
Huang
,
J. S.
, 2009, “
Heat and Mass Transfer for Soret and Dufour’s Effects on Hiemenz Flow Through Porous Medium Onto a Stretching Surface
,”
Int. J. Heat Mass Transfer
,
52
(
9-10
), pp.
2399
2406
.
19.
Cheng
,
C. Y.
, 2009, “
Soret and Dufour Effects on Natural Convection Heat and Mass Transfer From a Vertical Cone in a Porous Medium
,”
Int. Commun. Heat Mass Transfer
,
36
(
10
), pp.
1020
1024
.
20.
Murthy
,
S. V. S. S. N. V. G. K.
,
Kumar
,
B. V. R.
,
Chandra
,
P.
,
Sangwan
,
V.
, and
Nigam
,
M.
, 2011, “
A Study of Double Diffusive Free Convection From a Corrugated Vertical Surface in a Darcy Porous Medium Under Soret and Dufour Effects
,”
ASME J. Heat Transfer
,
133
(
9
),
092601
.
21.
Liao
,
S. J.
, 2003,
Beyond Perturbation, Introduction to Homotopy Analysis Method
,
Chapman and Hall
,
Boca Raton
.
22.
Liao
,
S. J.
, 2004, “
On the Homotopy Analysis Method for Nonlinear Problems
,”
Appl. Math. Comput.
,
147
(
2
), pp.
499
513
.
23.
Liao
,
S. J.
, 2006, “
An Analytic Solution of Unsteady Boundary-Layer Flows Caused by an Impulsively Stretching Plate
,”
Commun. Nonlinear Sci. Numer. Simul.
,
11
(
3
), pp.
326
339
.
24.
Hashim
,
I.
,
Abdulaziz
,
O.
, and
Momani
,
S.
, 2009, “
Homotopy Analysis Method for Fractional IVPs
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
(
3
), pp.
674
684
.
25.
Abbasbandy
,
S.
, and
Shivanian
,
E.
, 2010, “
Prediction of Multiplicity of Solutions of Nonlinear Boundary Value Problems: Novel Application of Homotopy Analysis Method
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
12
), pp.
3830
3846
.
26.
Abbasbandy
,
S.
, 2010, “
Homotopy Analysis Method for the Kawahara Equation
,”
Nonlinear Anal.: Real World Appl.
,
11
(
1
), pp.
307
312
.
27.
Yao
,
B.
, and
Chen
,
J.
, 2009, “
Series Solution to the Falkner–Skan Equation With Stretching Boundary
,”
Appl. Math. Comput.
,
208
(
1
), pp.
156
164
.
28.
Hayat
,
T.
,
Awais
,
M.
,
Asghar
,
S.
, and
Hendi
,
A. A.
, 2011, “
Analytic Solution for the Magnetohydrodynamic Rotating Flow of Jeffrey Fluid in a Channel
,”
ASME J. Fluid Eng.
,
133
(
6
),
061201
.
29.
Hayat
,
T.
, and
Awais
,
M.
, 2011, “
Three-Dimensional Flow of Upper-Convected Maxwell (UCM) Fluid
,”
Int. J. Numer. Methods Fluids
,
66
(
7
), pp.
875
884
.
30.
Domairry
,
G.
, and
Fazeli
,
M.
, 2009, “
Homotopy Analysis Method to Determine the Fin Efficiency of Convective Straight Fins With Temperature-Dependent Thermal Conductivity
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
(
2
), pp.
489
499
.
31.
Rashidi
,
M. M.
,
Domairry
,
G.
, and
Dinarvand
,
S.
, 2009, “
Approximate Solutions for the Burger and Regularized Long Wave Equations by Means of the Homotopy Analysis Method
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
(
3
), pp.
708
717
.
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