The present study investigates magnetic, first-order chemical reaction, Soret and Dufour effects on electrically conducting micropolar fluid flow between two circular cylinders. The inner and outer surfaces of the annular cylinder are maintained at different constant wall temperature where the outer cylinder is rotating and inner cylinder remains stationary. The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations (ODEs) using similarity transformations. The resulting equations are then solved for approximate analytical series solutions using homotopy analysis method (HAM). The effects of various parameters on the velocity, microrotation temperature and concentration are discussed and shown graphically.

References

References
1.
Aung
,
W.
,
Kakac
,
S.
, and
Shah
,
R. K.
,
1987
,
Handbook of Single-Phase Convective Heat Transfer
,
Wiley
,
New York
, Chap. 15.
2.
Jackson
,
J. D.
,
Cotton
,
M. A.
, and
Axcell
,
B. P.
,
1989
, “
Studies of Mixed Convection in Vertical Tubes
,”
Int. J. Heat Fluid Flow
,
10
, pp.
2
15
.10.1016/0142-727X(89)90049-0
3.
Taylor
G. I.
,
1923
, “
Stability of a Viscous Liquid Contained Between Two Rotating Cylinders
,”
Philos. Trans. R. Soc. London, Ser. A
,
223
, pp.
289
343
.10.1098/rsta.1923.0008
4.
Fusegi
T.
,
Farouk
B.
, and
Ball
K. S.
,
1986
, “
Mixed-Convection Flows Within a Horizontal Concentric Annulus With a Heated Rotating Inner Cylinder
,”
Numer. Heat Transfer
,
9
, pp.
591
604
.10.1080/10407788608913495
5.
Kataoka
K.
,
1986
, “
Taylor Vortices and Instabilities in Circular Couette Flows
,”
Encyclopaedia of Fluid Mechanics
,
N. P.
Cheremisinoff
, ed.,
Gulf
,
Houston, TX
.
6.
El-Shaarawi
M. A. I.
, and
Khamis
M.
,
1987
, “
Induced Flow in Uniformly Heated Vertical Annuli With Rotating Inner Walls
,”
Numer. Heat Transfer
,
12
, pp.
493
508
.10.1080/10407788708913599
7.
Kou
,
H. S.
, and
Huang
,
D. K.
,
1997
, “
Fully Developed Laminar Mixed Convection Through a Vertical Annular Duct Filled With Porous Media
,”
Int. Commun. Heat Mass Transfer
,
24
(
1
), pp.
99
110
.10.1016/S0735-1933(96)00109-1
8.
Kermlt L.
Holman
,
Sudhir. T.
Ashar
,
1971
, “
Mass Transfer in Concentric Rotating Cylinders With Surface Chemical Reaction in the Presence of Taylor Vortexes
,”
Chem. Eng. Sci.
,
26
, pp.
1817
1831
.10.1016/0009-2509(71)86026-8
9.
Pop
,
I.
,
Grosan
,
T.
, and
Cornelia
,
R.
,
2010
, “
Effect of Heat Generated by an Exothermic Reaction on the Fully Developed Mixed Convection Flow in a Vertical Channel
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
, pp.
471
474
.10.1016/j.cnsns.2009.04.010
10.
Shateyi
,
S.
,
Motsa
,
S. S.
, and
Sibanda
,
P.
,
2010
, “
Homotopy Analysis of Heat and Mass Transfer Boundary Layer Flow Through a Non-Porous Channel With Chemical Reaction and Heat Generation
,”
Can. J. of Chem. Engg.
,
88
, pp.
975
982
.10.1002/cjce.20366
11.
Kafoussias
N. G.
, and
Williams
E. W.
,
1995
, “
Thermal-Diffusion and Diffusion-Thermo Effects on Mixed Freeforced Convective and Mass Transfer Boundary Layer Flow With Temperature Dependent Viscosity
,”
Int. J. Eng. Sci.
,
33
(
9
), pp.
1369
1384
.10.1016/0020-7225(94)00132-4
12.
Awad
F.
, and
Sibanda
P.
,
2010
, “
Dufour and Soret Effects on Heat and Mass Transfer in a Micropolar Fluid in a Horizontal Channel
,”
WSEAS Trans. Heat Mass Transfer
,
5
, pp.
165
177
.
13.
Sudarsan Reddy
,
P.
,
Prasada Rao
,
D. R. V.
,
Mamatha
,
E.
, and
Srinivas
,
G.
,
2010
, “
Finite Element Analysis of Thermo-Diffusion and Diffusion-Thermo Effects on Convective Heat and Mass Transfer Flow Through a Porous Medium in Cylindrical Annulus in the Presence of Constant Heat Source
,”
Int. J. Appl. Math Mech.
,
6
(
7
), pp.
43
62
.
14.
Sulochana
,
C.
,
Gururaj
,
N.
, and
Devika
,
S.
,
2011
, “
Finite Element Analysis of Thermo-Diffusion Effect on Convective Heat and Mass Transfer Through a Porous Medium in Circular Annulus
,”
Int. J. Appl. Math Mech.
,
7
(
6
), pp.
80
101
.
15.
Takhar
,
H. S.
,
Ali
,
M. A.
, and
Soundalgekar
,
V. M.
,
1989
, “
Stability of MHD Couette Flow in a Narrow Gap Annulus
,”
Appl. Sci. Res.
,
46
, pp.
1
24
.10.1007/BF00420000
16.
Panja
,
S.
,
Sengupta
,
P. R.
, and
Debnath
,
L.
,
1996
, “
Hydromagnetic Flow of Reiner-Rivlin Fluid Between Two Coaxial Circular Cylinders With Porous Walls
,”
Comput. Math. Appl.
,
32
(
2
), pp.
1
4
.10.1016/0898-1221(96)00098-3
17.
KunugiLi
,
F. C. T.
, and
Serizawa
,
A.
,
2005
, “
MHD effect on Flow Structures and Heat Transfer Characteristics of Liquid Metal-Gas Annular Flow in a Vertical Pipe
,”
Int. J. Heat Mass Transfer
,
48
, pp.
2571
2581
.10.1016/j.ijheatmasstransfer.2004.12.041
18.
Siddiqa
,
S.
,
Hossain
,
Md. A.
,
Suvash
,
C. S.
,
2012
, “
Double Diffusive Magneto-Convection Fluid Flow in a Strong Cross Magnetic Field With Uniform Surface Heat and Mass Flux
,”
ASME J. Heat Transfer
,
134
(
11
), p.
114506
.10.1115/1.4007130
19.
Ericksen
,
J. C.
,
1960
, “
Anisotropic Fluids
,”
Arch. Ration. Mech. Anal.
4
, pp.
231
237
.10.1007/BF0028138910.1007/bf01502416
20.
Ericksen
,
J. C.
,
1960
Transversely Isotropic Fluids
,”
Colloid Polym. Sci
,
173
, pp.
117
122
.10.1007/bf01502416
21.
Eringen
,
A. C.
,
1966
, “
Theory of Micropolar Fluids
,”
J. Math. Mech.
16
, pp.
1
18
.
22.
Liao
,
S. J.
,
2003
,
Beyond Perturbation. Introduction to Homotopy Analysis Method
,
Chapman and Hall/CRC Press
,
Boca Raton, FL
.
23.
Liao
,
S. J.
,
2004
, “
On the Homotopy Analysis Method for Nonlinear Problems
,”
Appl. Math. Comput.
,
147
(
2
), pp.
499
513
.10.1016/S0096-3003(02)00790-7
24.
Liao
,
S. J.
,
2010
, “
An Optimal Homotopy-Analysis Approach for Strongly Nonlinear Differential Equations
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
, pp.
2003
2016
.10.1016/j.cnsns.2009.09.002
25.
Rashidi
,
M. M.
,
Mohimanian pour
,
S. A.
,
Abbasbandy
,
S.
,
2011
, “
Analytic Approximate Solutions for Heat Transfer of a Micropolar Fluid Through a Porous Medium With Radiation
,”
Commun. Nonlinear Sci. Numer. Simul.
,
16
, pp.
1874
1889
.10.1016/j.cnsns.2010.08.016
26.
Si
,
X.-H.
,
Zheng
,
L.-C.
,
Zhang
,
X.-X.
, and
Chao
,
Y.
,
2011
, “
Homotopy Analysis Solutions for the Asymmetric Laminar Flow in a Porous Channel With Expanding or Contracting Walls
,”
Acta Mech. Sin.
,
27
(
2
), pp.
208
214
.10.1007/s10409-011-0430-3
27.
Kazakia
,
Y.
, and
Ariman
,
T.
,
1971
, “
Heat-Conducting Micropolar Fluids
,”
Rheol. Acta
,
10
, pp.
319
325
.10.1007/BF01993705
28.
Ramkzssoon
,
H.
, and
Majumdar
,
S. R.
,
1977
, “
Unsteady Flow of a Micropolar Fluid Between Two Concentric Circular Cylinders
,”
Can. J Chem Eng.
,
55
, pp.
408
413
.10.1002/cjce.5450550408
29.
van Gorder
,
R.A.
, and
Vajravelu
,
K.
,
2009
, “
On the Selection of Auxiliary Functions, Operators, and Convergence Control Parameters in the Application of the Homotopy Analysis Method to Nonlinear Differential Equations: A General Approach
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
, pp.
4078
4089
.10.1016/j.cnsns.2009.03.008
30.
Postelnicu
,
A.
,
2010
, “
Heat and Mass Transfer by Natural Convection at a Stagnation Point in a Porous Medium Considering Soret and Dufour Effects
,”
Heat Mass Transfer
,
46
, pp.
831
840
.10.1007/s00231-010-0633-3
31.
Benano-Melly
,
L. B.
,
Caltagirone
,
J. P.
,
Faissat
,
B.
,
Montel
,
F.
, and
Costeseque
,
P.
,
2001
,”
Modelling Soret Coefficient Measurement Experiments in Porous Media Considering Thermal and Solutal Convection
,”
Int. J. Heat Mass Transfer
,
44
, pp.
1285
1297
.10.1016/S0017-9310(00)00183-6
32.
Anghel
,
M.
,
Takhar
,
H. S.
, and
Pop
,
I.
,
2000
, “
Dufour and Soret Effects on Free Convection Boundary-Layer Over a Vertical Surface Embedded in a Porous Medium
,”
Studia Universitatis Babes-Bolyai, Mathematica
,
XLV
, pp.
11
22
.
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