Abstract

Little is known on the three-dimensional flow of a couple stress Casson fluid conveying nanoparticles when the significance of Lorentz force, chaotic gesture of those minute particles, and thermophoresis are significant. The intent of this investigation is to focus on the flow of such fluid along a horizontal surface due to dual stretching and internal heating. A zero nanoparticle mass flux condition is employed at the surface, which specifies that the nanoparticles’ fraction is submissively measured. The dimensional nonlinear equations are reduced into a system of coupled nonlinear ordinary differential equations by employing scaling analysis and later they are solved numerically. The results are discussed graphically for various emerged physical parameters through different plots. The results in the absence of stretching ratio factor indicate that the heat absorption parameter and Prandtl number accelerate the heat transfer rate. The temperature of the non-Newtonian couple stress fluid is found to be higher than that of viscous case. It may be suggested that the Casson couple stress nanofluid can be substituted for the corresponding viscous fluid in industrial applications for greater heat transfer. The outcomes are closely matched with the studies available in the literature as a limiting case.

References

1.
Hayat
,
T.
, and
Nadeem
,
S.
,
2018
, “
An Optimal Solution of Cattaneo–Christov Heat Flux Model and Chemical Processes for 3D Flow of Eyring–Powell Fluid
,”
J. Braz. Soc. Mech. Sci. Eng.
,
40
(
538
), pp.
1
9
. 10.1007/s40430-018-1451-7
2.
Moatimid
,
G. M.
, and
Hassan
,
M. A.
,
2017
, “
Convection Instability of Non-Newtonian Walter’s Nanofluid Along a Vertical Layer
,”
J. Egypt. Math. Soc.
,
25
(
2
), pp.
220
229
. 10.1016/j.joems.2016.09.001
3.
Saleem
,
S.
,
Firdous
,
H.
,
Nadeem
,
S.
, and
Khan
,
A. U.
,
2019
, “
Convective Heat and Mass Transfer in Magneto Walter’s B Nanofluid Flow Induced by a Rotating Cone
,”
Arabian J. Sci. Eng.
,
44
(
2
), pp.
1515
1523
. 10.1007/s13369-018-3598-z
4.
Gaffar
,
S. A.
,
Ramachandra Prasad
,
V.
, and
Vijaya
,
B.
,
2017
, “
Computational Study of Non-Newtonian Eyring–Powell Fluid From a Vertical Porous Plate With Biot Number Effects
,”
J. Braz. Soc. Mech. Sci. Eng.
,
39
(
7
), pp.
2747
2765
. 10.1007/s40430-017-0761-5
5.
Rehman
,
K. U.
,
Malik
,
M. Y.
,
Zehra
,
I.
, and
Alqarni
,
M. S.
,
2019
, “
Group Theoretical Analysis for MHD Flow Fields: A Numerical Result
,”
J. Braz. Soc. Mech. Sci. Eng.
,
41
(
3
), pp.
156
163
. 10.1007/s40430-019-1662-6
6.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
,
128
(
3
), pp.
240
250
. 10.1115/1.2150834
7.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2013
, “
The Cheng–Minkowycz Problem for Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid: A Revised Model
,”
Int. J. Heat Mass Transfer
,
65
, pp.
682
685
. 10.1016/j.ijheatmasstransfer.2013.06.054
8.
Najiyah
,
S. K.
,
Norihan
,
M. A.
,
Roslinda
,
N.
,
Ezad Hafidz
,
H.
,
Nadihah
,
W.
, and
Pop
,
I.
,
2019
, “
A Stability Analysis for Magnetohydrodynamics Stagnation Point Flow With Zero Nanoparticles Flux Condition and Anisotropic Slip
,”
Energies
,
12
(
7
), p.
1268
. 10.3390/en12071268
9.
Rehman
,
S. U.
,
Haq
,
R. U.
,
Khan
,
Z. H.
, and
Lee
,
C.
,
2016
, “
Entropy Generation Analysis for Non-Newtonian Nanofluid With Zero Normal Flux of Nanoparticles at the Stretching Surface
,”
J. Taiwan Inst. Chem. Eng.
,
63
, pp.
226
235
. 10.1016/j.jtice.2016.03.006
10.
Uddin
,
M. A.
,
Khan
,
S.
,
Ullah
,
S.
,
Islam
,
M.
, and
Israr
,
F.
,
2018
, “
Hussain, Characteristics of Buoyancy Force on Stagnation Point Flow With Magneto-Nanoparticles and Zero Mass Flux Condition
,”
Results Phys.
,
8
, pp.
160
168
. 10.1016/j.rinp.2017.10.038
11.
Jusoh
,
R.
,
Nazar
,
R.
, and
Pop
,
I.
,
2018
, “
Three-Dimensional Flow of a Nanofluid Over a Permeable Stretching/Shrinking Surface With Velocity Slip: A Revised Model
,”
Phys. Fluids
,
30
(
3
), p.
03360
. 10.1063/1.5021524
12.
Casson
,
N.
,
1959
, “A Flow Equation for Pigment-Oil Suspensions of the Printing Ink Type,”
Rheology of Disperse Systems
,
C. C.
Mill
, ed.,
Pergamon Press
,
Oxford
, pp.
84
104
.
13.
Dash
,
R. K.
,
Mehta
,
K. N.
, and
Jayaraman
,
G.
,
1996
, “
Casson Fluid Flow in a Pipe Filled With a Homogeneous Porous Medium
,”
Int. J. Eng. Sci.
,
34
(
10
), pp.
1145
1566
. 10.1016/0020-7225(96)00012-2
14.
Hymavathi
,
T.
, and
Sridhar
,
W.
,
2018
, “
Numerical Solution to Boundary Layer Flow and Mass Transfer of Casson Fluid Over a Porous Stretching Sheet With Chemical Reaction and Suction
,”
J. Comput. Math. Sci.
,
9
(
6
), pp.
599
608
. 10.29055/jcms/794
15.
Sharada
,
K.
, and
Shankar
,
B.
,
2016
, “
Three-Dimensional MHD Mixed Convection Casson Fluid Flow Over an Exponential Stretching Sheet With the Effect of Heat Generation
,”
Br. J. Math. Comput. Sci.
,
19
(
6
), pp.
1
8
. 10.9734/BJMCS/2016/29454
16.
Butt
,
A. S.
,
Tufail
,
M. N.
, and
Ali
,
A.
,
2016
, “
Three-Dimensional Flow of a Magnetohydrodynamic Casson Fluid Over an Unsteady Stretching Sheet Embedded Into a Porous Medium
,”
J. Appl. Mech. Tech. Phys.
,
57
(
2
), pp.
283
292
. 10.1134/S0021894416020115
17.
Stokes
,
V. K.
,
1984
,
Theories of Fluids With Microstructure: An Introduction
,
Springer
,
Berlin
.
18.
Stokes
,
V. K.
,
1966
, “
Couple Stresses in Fluids
,”
Phys. Fluids
,
9
(
9
), pp.
1709
1715
. 10.1063/1.1761925
19.
Cowin
,
S. C.
,
1974
, “
The Theory of Polar Fluids
,”
Adv. Appl. Mech.
,
14
, pp.
82
279
.
20.
Thammanna
,
G. T.
,
Ganesh Kumar
,
K.
,
Gireesha
,
B. J.
,
Ramesh
,
G. K.
, and
Prasannakumara
,
B. C.
,
2017
, “
Three Dimensional MHD Flow of Couple Stress Casson Fluid Past an Unsteady Stretching Surface With Chemical Reaction
,”
Results Phys.
,
7
, pp.
4104
4110
. 10.1016/j.rinp.2017.10.016
21.
Lopez
,
G.
,
Ibanez
,
J.
, and
Pantoja
,
J.
,
2017
, “
Moreira and O. Lastres, Entropy Generation Analysis of MHD Nanofluid Flow in a Porous Vertical Microchannel With Nonlinear Thermal Radiation, Slip Flow and Convective-Radiative Boundary Conditions
,”
Int. J. Heat Mass Transfer
,
107
, pp.
982
994
. 10.1016/j.ijheatmasstransfer.2016.10.126
22.
Ijaz
,
S.
, and
Nadeem
,
S.
,
2018
, “
Shape Factor and Sphericity Features Examination of Cu and Cu-Al2O3/Blood Through Atherosclerotic Artery Under the Impact of Wall Characteristic
,”
J. Mol. Liq.
,
271
(
1
), pp.
361
372
. 10.1016/j.molliq.2018.08.122
23.
Hayat
,
T.
,
Qayyum
,
S.
,
Imtiaz
,
M.
, and
Alsaedi
,
A.
,
2016
, “
Comparative Study of Silver and Copper Water Nanofluids With Mixed Convection and Nonlinear Thermal Radiation
,”
Int. J. Heat Mass Transfer
,
102
, pp.
723
732
. 10.1016/j.ijheatmasstransfer.2016.06.059
24.
Ramzan
,
M.
,
Chung
,
J. D.
, and
Ullah
,
N.
,
2017
, “
Radiative Magnetohydrodynamic Nanofluid Flow Due to Gyrotactic Microorganisms With Chemical Reaction and Non-Linear Thermal Radiation
,”
Int. J. Mech. Sci.
,
130
, pp.
31
40
. 10.1016/j.ijmecsci.2017.06.009
25.
Makinde
,
O. D.
, and
Animasaun
,
I. L.
,
2016
, “
Bioconvection in MHD Nanofluid Flow With Nonlinear Thermal Radiation and Quartic Autocatalysis Chemical Reaction Past an Upper Surface of a Paraboloid of Revolution
,”
Int. J. Therm. Sci.
,
109
, pp.
159
171
. 10.1016/j.ijthermalsci.2016.06.003
26.
Hayat
,
T.
, and
Nadeem
,
S.
,
2018
, “
An Improvement in Heat Transfer for Rotating Flow of Hybrid Nanofluid: A Numerical Study
,”
Can. J. Phys.
,
96
(
12
), pp.
1420
1430
. 10.1139/cjp-2017-0801
27.
Tarakaramu
,
N.
, and
Satya Narayana
,
P. V.
,
2019
, “
Nonlinear Thermal Radiation and Joule Heating Effects on MHD Stagnation Point Flow of Nanofluid Over a Convectively Heated Stretching Surface
,”
J. Nanofluids
,
5
, pp.
1066
1075
. 10.1166/jon.2019.1651
28.
Satyanarayana
,
P. V.
,
Tarakaramu
,
N.
,
Makinde
,
O. D.
,
Venkateswarlu
,
B.
, and
Sarojamma
,
G.
,
2018
, “
MHD Stagnation Point Flow of Viscoelastic Nanofluid Past a Convectively Heated Stretching Surface
,”
Defect Diffus. Forum
,
387
, pp.
106
120
. 10.4028/www.scientific.net/DDF.387.106
29.
Nadeem
,
S.
, and
Abbas
,
N.
,
2019
, “
On Both MHD and Slip Effect in Micropolar Hybrid Nanofluid Past a Circular Cylinder Under Stagnation Point Region
,”
Can. J. Phys.
,
97
(
4
), pp.
392
399
. 10.1139/cjp-2018-0173
30.
Tarakaramu
,
N.
, and
Satya Narayana
,
P. V.
,
2019
, “
Chemical Reaction Effects on Bio-Convection Nanofluid Flow Between Two Parallel Plates in Rotating System: A Numerical Study
,”
J. Appl. Comput. Mech.
,
5
(
1
), pp.
791
803
.
31.
Pushpalatha
,
K.
,
Ramana Reddy
,
J. V.
,
Sugunamma
,
V.
, and
Sandeep
,
N.
,
2017
, “
Numerical Study of Chemically Reacting Unsteady Casson Fluid Flow Past a Stretching Surface With Cross Diffusion and Thermal Radiation
,”
Open Eng.
,
7
(
1
), pp.
69
76
. 10.1515/eng-2017-0013
32.
Hayat
,
T.
,
Kiran
,
A.
,
Imtiaz
,
M.
, and
Alsaedi
,
A.
,
2017
, “
Unsteady Flow of Carbon Nanotubes With Chemical Reaction and Cattaneo–Christov Heat Flux Model
,”
Results Phys.
,
7
, pp.
823
831
. 10.1016/j.rinp.2017.01.031
33.
Satya Narayana
,
P. V.
,
Akshit
,
S. M.
,
Ghori
,
J. P.
, and
Venkateswarlu
,
B.
,
2017
, “
Thermal Radiation Effects on an Unsteady MHD Nanofluid Flow Over a Stretching Sheet With Non-Uniform Heat Source/Sink
,”
J. Nanofluids
,
8
, pp.
1
5
. 10.1166/jon.2017.1374
34.
Ismail
,
N. S.
,
Arifin
,
N. M.
,
Bachok
,
N.
, and
Mahiddin
,
N.
,
2017
, “
The Stagnation-Point Flow Towards a Shrinking Sheet With Homogeneous–Heterogeneous Reactions Effects: A Stability Analysis
,”
AIP Conf. Proc.
,
1795
(
1
), pp.
1
9
. 10.1063/1.4972153
35.
Nakamura
,
M.
, and
Sawada
,
T.
,
1988
, “
Numerical Study on the Flow of a Non-Newtonian Fluid Through an Axisymmetric Stenosis
,”
ASME J. Biomech. Eng.
,
110
(
2
), pp.
137
143
. 10.1115/1.3108418
36.
Hayat
,
T.
,
Muhammad
,
T.
,
Alsaedi
,
A.
, and
Alhuthali
,
M. S.
,
2015
, “
Magnetohydrodynamic Three-Dimensional Flow of Viscoelastic Nanofluid in the Presence of Nonlinear Thermal Radiation
,”
J. Magn. Magn. Mater.
,
385
(
1
), pp.
222
229
. 10.1016/j.jmmm.2015.02.046
37.
Shah
,
Z.
,
Dawar
,
A.
,
Alzahrani
,
E. O.
,
Kumam
,
P.
,
Jabbar Khan
,
A.
, and
Islam
,
S.
,
2019
, “
Hall Effect on Couple Stress 3D Nanofluid Flow Over an Exponentially Stretched Surface With Cattaneo Christov Heat Flux Model
,”
IEEE Access
,
7
, pp.
64844
64855
. 10.1109/access.2019.2916162
38.
Ramzan
,
M.
,
Sheikholeslami
,
M.
,
Saeed
,
M.
, and
Chung
,
J. D.
,
2019
, “
On the Convective Heat and Zero Nanoparticle Mass Flux Conditions in the Flow of 3D MHD Couple Stress Nanofluid Over an Exponentially Stretched Surface
,”
Sci. Rep.
,
9
(
1
), pp.
1
13
. 10.1038/s41598-018-37186-2
39.
Animasaun
,
I. L.
,
Koriko
,
O. K.
,
Mahanthesh
,
B.
, and
Dogonchi
,
A. S.
,
2019
, “
A Note on the Significance of Quartic Autocatalysis Chemical Reaction on the Motion of Air Conveying Dust Particles
,”
Zeitschrift Für Naturforschung A
,
74
(
10
), pp.
879
904
. 10.1515/zna-2019-0180
40.
Animasaun
,
I. L.
,
Ibraheem
,
R. O.
,
Mahanthesh
,
B.
, and
Babatunde
,
H. A.
,
2019
, “
A Meta-Analysis on the Effects of Haphazard Motion of Tiny/Nano-Sized Particles on the Dynamics and Other Physical Properties of Some Fluids
,”
Chin. J. Phys.
,
60
, pp.
676
687
. 10.1016/j.cjph.2019.06.007
41.
Rahbari
,
A.
,
Fakour
,
M.
,
Hamzehnezhad
,
A.
,
Vakilabadi
,
M. A.
, and
Ganji
,
D. D.
,
2017
, “
Heat Transfer and Fluid Flow of Blood With Nanoparticles Through Porous Vessels in a Magnetic Field: A Quasi-One Dimensional Analytical Approach
,”
Math. Biosci.
,
283
, pp.
38
47
. 10.1016/j.mbs.2016.11.009
42.
Wang
,
Y.
,
1984
, “
The Three-Dimensional Flow Due to a Stretching Flat Surface
,”
Phys. Fluids
,
7
(
1915
), pp.
1
4
. 10.1063/1.864868
43.
Ariel
,
P. D.
,
2003
, “
Generalized Three-Dimensional Flow Due to a Stretching Sheet
,”
ZAMM
,
83
(
12
), pp.
844
852
. 10.1002/zamm.200310052
44.
Ghosh
,
S.
,
Mukhopadhyay
,
S.
, and
Hayat
,
T.
,
2018
, “
Couple Stress Effects on Three Dimensional Flow of Magnetite-Water Based Nanofluid Over an Extended Surface in Presence of Non-Linear Thermal Radiation
,”
Int. J. Appl. Comput. Math.
,
4
(
1
), pp.
1
18
. 10.1007/s40819-017-0443-0
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