Based on Buongiorno's theory and Cauchy equations of motion, a model is developed to examine homogeneous–heterogeneous reactions in boundary layer flow of a nanofluid over a stretching sheet in which a uniform magnetic field is added perpendicular to the flow direction. We apply the shooting method and the fourth-order Runge–Kutta integration to obtain multiple solutions of nonlinear ordinary differential equations with various physical parameters. Results show that nanofluids play significant roles in the procedures of homogeneous and heterogeneous reactions, which may help maintain the stability of chemical reactions. In addition, the terms related to Maxwell fluid either have effect on stability of the system; furthermore, the increasing elastic and magnetic parameters delay the appearance of bifurcation points.

References

1.
Chaudhary
,
M. A.
, and
Merkin
,
J. H.
,
1995
, “
A Simple Isothermal Model for Homogeneous-Heterogeneous Reactions in Boundary-Layer Flow—Part I: Equal Diffusivities
,”
Fluid Dyn. Res.
,
16
(
6
), pp.
311
333
.
2.
Chaudhary
,
M. A.
, and
Merkin
,
J. H.
,
1995
, “
A Simple Isothermal Model for Homogeneous-Heterogeneous Reactions in Boundary-Layer Flow—Part II: Different Diffusivities for Reactant and Autocatalyst
,”
Fluid Dyn. Res.
,
16
(
6
), pp.
335
359
.
3.
Merkin
,
J. H.
,
1996
, “
A Model for Isothermal Homogeneous-Heterogeneous Reactions in Boundary-Layer Flow
,”
Math. Comput. Modell.
,
24
(
8
), pp.
125
136
.
4.
Xu
,
H.
,
2017
, “
A Homogeneous-Heterogeneous Reaction Model for Heat Fluid Flow in the Stagnation Region of a Plane Surface
,”
Int. Commun. Heat Mass Transfer
,
87
, pp.
112
117
.
5.
Bachok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2011
, “
On the Stagnation-Point Flow Towards a Stretching Sheet With Homogeneous-Heterogeneous Reactions Effects
,”
Commun. Nonlinear Sci. Numer. Simul.
,
16
(
11
), pp.
4296
4302
.
6.
Khan
,
W. A.
, and
Pop
,
I.
,
2010
, “
Flow Near the Two-Dimensional Stagnation-Point on an Infinite Permeable Wall With a Homogeneous–Heterogeneous Reaction
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
11
), pp.
3435
3443
.
7.
Raju
,
C. S. K.
,
Sandeep
,
N.
, and
Saleem
,
S.
,
2016
, “
Effects of Induced Magnetic Field and Homogeneous-Heterogeneous Reactions on Stagnation Flow of a Casson Fluid
,”
Eng. Sci. Technol.
,
19
(
2
), pp.
875
887
.
8.
Khan
,
M. I.
,
Hayat
,
T.
,
Khan
,
M. I.
, and
Alsaedi
,
A.
,
2017
, “
A Modified Homogeneous-Heterogeneous Reactions for MHD Stagnation Flow With Viscous Dissipation and Joule Heating
,”
Int. J. Heat Mass Transfer
,
113
, pp.
310
317
.
9.
Choi
,
S. U. S.
,
1995
, “
Enhancing Thermal Conductivity of Fluids With Nanoparticles
,” ASME International Mechanical Engineering Congress and Exposition, San Francisco, CA, Nov. 12–17, pp.
99
105
.
10.
Rehman
,
T.
,
Ali
,
H. M.
,
Janjua
,
M. M.
,
Sajjad
,
U.
, and
Yan
,
W. M.
,
2019
, “
A Critical Review on Heat Transfer Augmentation of Phase Change Materials Embedded With Porous Materials/Foams
,”
Int. J. Heat Mass Transfer
,
135
, pp.
649
673
.
11.
Sajid
,
M. U.
, and
Ali
,
H. M.
,
2019
, “
Recent Advances in Application of Nanofluids in Heat Transfer Devices: A Critical Review
,”
Renewable Sustainable Energy Rev.
,
103
, pp.
556
592
.
12.
Rehman
,
T.
, and
Ali
,
H. M.
,
2018
, “
Experimental Investigation on Paraffin Wax Integrated With Copper Foam Based Heat Sinks for Electronic Components Thermal Cooling
,”
Int. Commun. Heat Mass Transfer
,
98
, pp.
155
162
.
13.
Khan
,
M. S.
,
Abid
,
M.
,
Ali
,
H. M.
,
Amber
,
K. P.
,
Bashir
,
M. A.
, and
Javed
,
S.
,
2019
, “
Comparative Performance Assessment of Solar Dish Assisted s-CO2 Brayton Cycle Using Nanofluids
,”
Appl. Therm. Eng.
,
148
(
5
), pp.
295
306
.
14.
Qureshi
,
Z. A.
,
Ali
,
H. M.
, and
Khushnood
,
S.
,
2018
, “
Recent Advances on Thermal Conductivity Enhancement of Phase Change Materials for Energy Storage System: A Review
,”
Int. J. Heat Mass Transfer
,
127
(
Pt C
), pp.
838
856
.
15.
Khan
,
M. M. A.
,
Ibrahim
,
N. I.
,
Mahbubul
,
I. M.
,
Ali
,
H. M.
,
Saidur
,
R.
, and
Al-Sulaiman
,
F. A.
,
2018
, “
Evaluation of Solar Collector Designs With Integrated Latent Heat Thermal Energy Storage: A Review
,”
Sol. Energy
,
166
(
15
), pp.
334
350
.
16.
Mahbubul
,
I. M.
,
Khan
,
M. M. A.
,
Ibrahim
,
N. I.
,
Ali
,
H. M.
,
Al-Sulaiman
,
F. A.
, and
Saidur
,
R.
,
2018
, “
Carbon Nanotube Nanofluid in Enhancing the Efficiency of Evacuated Tube Solar Collector
,”
Renewable Energy
,
121
, pp.
36
44
.
17.
Ali
,
H. M.
,
Arshad
,
A.
,
Jabbal
,
M.
, and
Verdin
,
P. G.
,
2018
, “
Thermal Management of Electronics Devices With PCMs Filled Pin-Fin Heat Sinks: A Comparison
,”
Int. J. Heat Mass Transfer
,
117
, pp.
1199
1204
.
18.
Arshad
,
A.
,
Ali
,
H. M.
,
Khushnood
,
S.
, and
Jabbal
,
M.
,
2018
, “
Experimental Investigation of PCM Based Round Pin-Fin Heat Sinks for Thermal Management of Electronics: Effect of Pin-Fin Diameter
,”
Int. J. Heat Mass Transfer
,
117
, pp.
861
872
.
19.
Arshad
,
A.
,
Ali
,
H. M.
,
Khushnood
,
S.
, and
Jabbal
,
M.
,
2017
, “
Experimental Passive Electronics Cooling: Parametric Investigation of Pin-Fin Geometries and Efficient Phase Change Materials
,”
Int. J. Heat Mass Transfer
,
115
(
Pt. B
), pp.
251
263
.
20.
Rama
,
G.
,
Reddy
,
S.
, and
Chamkha
,
A. J.
,
2011
, “
Natural Convective Boundary Layer Flow Over a Nonisothermal Vertical Plate Embedded in a Porous Medium Saturated With a Nanofluid
,”
Nanoscale Microscale Thermophys. Eng.
,
15
(
2
), pp.
81
94
.
21.
Reddy
,
C. R.
,
Murthy
,
P. V. S. N.
,
Chamkha
,
A. J.
, and
Rashad
,
A. M.
,
2013
, “
Soret Effect on Mixed Convection Flow in a Nanofluid Under Convective Boundary Condition
,”
Int. J. Heat Mass Transfer
,
64
, pp.
384
392
.
22.
Chamkha
,
A. J.
, and
Khaled
,
A. R. A.
,
2000
, “
Similarity Solutions for Hydromagnetic Mixed Convection Heat and Mass Transfer for Hiemenz Flow Through Porous Media
,”
Int. J. Num. Methods Heat Fluid Flow
,
10
(
1
), pp.
94
115
.
23.
Xuan
,
Y. M.
, and
Roetzel
,
W.
,
2000
, “
Conceptions for Heat Transfer Correlation of Nanofluids
,”
Int. J. Heat Transfer
,
43
(
19
), pp.
3701
3707
.
24.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
,
128
(
3
), pp.
240
250
.
25.
Kameswaran
,
P. K.
,
Shaw
,
S.
,
Sibanda
,
P.
, and
Murthy
,
P. V. S. N.
,
2013
, “
Homogeneous-Heterogeneous Reactions in a Nanofluid Flow Due to a Porous Stretching Sheet
,”
Int. J. Heat Mass Transfer
,
57
(
2
), pp.
465
472
.
26.
Zhao
,
Q. K.
,
Xu
,
H.
, and
Tao
,
L. B.
,
2016
, “
Homogeneous-Heterogeneous Reactions in Boundary-Layer Flow of a Nanofluid Near the Forward Stagnation Point of a Cylinder
,”
ASME J. Heat Transfer
,
139
(
3
), p.
034502
.
27.
Xu
,
N. L.
,
Xu
,
H.
, and
Raees
,
A.
,
2018
, “
Homogeneous-Heterogeneous Reactions in Flow of Nanofluids Near Stagnation Region of a Plane Surface: The Buongiorno's Model
,”
Int. J. Heat Mass Transfer
,
125
, pp.
604
609
.
28.
Raees
,
A.
,
Wang
,
R. Z.
, and
Xu
,
H.
,
2018
, “
A Homogenous-Heterogeneous Model for Mixed Convection in Gravity-Driven Film Flow of Nanofluids
,”
Int. Comm. Heat Mass Transfer
,
95
, pp.
19
24
.
29.
Sadeghy
,
K.
,
Najafi
,
A. H.
, and
Saffaripour
,
M.
,
2005
, “
Sakiadis Flow of an Upper-Convected Maxwell Fluid
,”
Int. J. Nonlinear Mech.
,
40
(
9
), pp.
1220
1228
.
30.
Afify
,
A. A.
, and
Elgazery
,
N. S.
,
2016
, “
Effect of a Chemical Reaction on Magnetohydrodynamic Boundary Layer Flow of a Maxwell Fluid Over a Stretching Sheet With Nanoparticles
,”
Particuology
,
29
, pp.
154
161
.
31.
Ramzan
,
M.
,
Bilal
,
M.
, and
Chung
,
J. D.
,
2017
, “
Influence of Homogeneous-Heterogeneous Reactions on MHD 3D Maxwell Fluid Flow With Cattaneo-Christov Heat Flux and Convective Boundary Condition
,”
J. Mol. Liq.
,
230
, pp.
415
422
.
32.
Reddy
,
P. S.
,
Sreedevi
,
P.
, and
Chamkha
,
A. J.
,
2017
, “
MHD Boundary Layer Flow, Heat and Mass Transfer Analysis Over a Rotating Disk Through Porous Medium Saturated by Cu-Water and Ag-Water Nanofluid With Chemical Reaction
,”
Powder Technol.
,
307
, pp.
46
55
.
33.
Reddy
,
P. S.
, and
Chamkha
,
A. J.
,
2016
, “
Soret and Dufour Effects on MHD Convective Flow of Al2O3C–Water and TiO2C–Water Nanofluids Past a Stretching Sheet in Porous Media With Heat Generation/Absorption
,”
Adv. Powder Technol.
,
27
(
4
), pp.
1207
1218
.
34.
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
.
35.
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
.
36.
Magyari
,
E.
, and
Chamkha
,
A. J.
,
2008
, “
Exact Analytical Results for the Thermosolutal MHD Marangoni Boundary Layers
,”
Int. J. Therm. Sci.
,
47
(
7
), pp.
848
857
.
37.
Khedr
,
M. E. M.
,
Chamkha
,
A. J.
, and
Bayomi
,
M.
,
2009
, “
MHD Flow of a Micropolar Fluid Past a Stretched Permeable Surface With Heat Generation or Absorption
,”
Nonlinear Anal.: Modell. Control
,
14
(
1
), pp.
27
40
.http://alichamkha.net/wp-content/uploads/2012/10/196.pdf
38.
Takhar
,
H. S.
,
Chamkha
,
A. J.
, and
Nath
,
G.
,
2002
, “
MHD Flow Over a Moving Plate in a Rotating Fluid With Magnetic Field, Hall Currents and Free Stream Velocity
,”
Int. J. Eng. Sci.
,
40
(
13
), pp.
1511
1527
.
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