The stagnation-point flow and heat transfer toward a stretching/shrinking sheet in a nanofluid containing gyrotactic microorganisms with suction are investigated. Using a similarity transformation, the nonlinear system of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a shooting method. The skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms profiles are analyzed subject to several parameters of interest, namely suction parameter, thermophoresis parameter, Brownian motion parameter, Lewis number, Schmidt number, bioconvection Péclet number, and the stretching/shrinking parameter. It is found that dual solutions exist for a certain range of the stretching/shrinking parameter for both shrinking and stretching cases. The results indicate that the skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms increase with suction effect. It is also observed that suction widens the range of the stretching/shrinking parameter for which the solution exists.

References

1.
Fang
,
T.
,
Yao
,
S.
,
Zhang
,
J.
, and
Aziz
,
A.
,
2010
, “
Viscous Flow Over a Shrinking Sheet With a Second Order Slip Flow Model
,”
Commun. Nonlinear Sci. Numer. Simulat.
,
15
, pp.
1831
1842
.10.1016/j.cnsns.2009.07.017
2.
Sparrow
,
E. M.
, and
Abraham
,
J. P.
,
2005
, “
Universal Solutions for the Streamwise Variation of the Temperature of a Moving Sheet in the Presence of a Moving Fluid
,”
Int. J. Heat Mass Transfer
,
48
, pp.
3047
3056
.10.1016/j.ijheatmasstransfer.2005.02.028
3.
Liao
,
S. J.
,
2005
, “
A New Branch of Solutions of Boundary-Layer Flows Over a Stretching Flat Plate
,”
Int. J. Heat Mass Transfer
,
49
, pp.
2529
2539
.10.1016/j.ijheatmasstransfer.2005.01.005
4.
Liao
,
S. J.
,
2007
, “
A New Branch of Solution of Boundary-Layer Flows Over a Permeable Stretching Plate
,”
Int. J. Nonlinear Mech.
,
42
, pp.
819
830
.10.1016/j.ijnonlinmec.2007.03.007
5.
Wang
,
C. Y.
,
1991
, “
Exact Solutions of The Steady State Navier–Stokes Equations
,”
Ann. Rev. Fluid Mech.
,
23
, pp.
159
177
.10.1146/annurev.fl.23.010191.001111
6.
Choi
,
S. U. S.
,
1995
, “
Enhancing Thermal Conductivity of Fluids With Nanoparticles
,”
Developments and Applications of Non-Newtonian Flows
, Vol.
231
,
D. A.
Singer
and
H. P.
Wang
, eds.,
American Society of Mechanical Engineers
,
New York
, pp.
99
105
.
7.
Choi
,
S. U. S.
,
Zhang
,
Z. G.
,
Yu
,
W.
,
Lockwood
,
F. E.
, and
Grulke
,
E. A.
,
2001
, “
Anomalously Thermal Conductivity Enhancement in Nanotube Suspensions
,”
Appl. Phys. Lett.
,
79
, pp.
2252
2254
.10.1063/1.1408272
8.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
,
128
, pp.
240
250
.10.1115/1.2150834
9.
Das
,
S. K.
,
Choi
,
S. U. S.
,
Yu
,
W.
, and
Pradeep
,
T.
,
2007
,
Nanofluids: Science and Technology
,
Wiley
,
Hoboken, NJ
.
10.
Kakaç
,
S.
, and
Pramuanjaroenkij
,
A.
,
2009
, “
Review of Convective Heat Transfer Enhancement With Nanofluids
,”
Int. J. Heat Mass Transfer
,
52
, pp.
3187
3196
.10.1016/j.ijheatmasstransfer.2009.02.006
11.
Wong
,
K. V.
, and
Leon
,
O. D.
,
2010
, “
Applications of Nanofluids: Current and Future
,”
Adv. Mech. Eng.
,
11
pp.10.1155/2010/519659
12.
Saidur
,
R.
,
Leong
,
K. Y.
, and
Mohammad
,
H. A.
,
2011
, “
A Review on Applications and Challenges of Nanofluids
,”
Renewable Sustainable Energy Rev.
,
15
, pp.
1646
1668
.10.1016/j.rser.2010.11.035
13.
Wen
,
D.
,
Lin
,
G.
,
Vafaei
,
S.
, and
Zhang
K.
,
2011
, “
Review of Nanofluids for Heat Transfer Applications
,”
Particuology
,
7
, pp.
141
150
.10.1016/j.partic.2009.01.007
14.
Mahian
,
O.
,
Kianifar
,
A.
,
Kalogirou
,
S. A.
,
Pop
,
I.
, and
Wongwises
,
S.
,
2013
, “
A review of the Applications of Nanofluids in Solar Energy
,”
Int. J. Heat Mass Transfer
,
57
, pp.
582
594
.10.1016/j.ijheatmasstransfer.2012.10.037
15.
Nield
,
D. A.
, and
Bejan
,
A.
,
2013
,
Convection in Porous Media
, 4th ed.,
Springer
,
New York
.
16.
Kuznetsov
,
A. V.
, and
Avramenko
,
A. A.
,
2004
, “
Effect of Small Particles on the Stability of Bioconvection in a Suspension of Gyrotactic Microorganisms in a Layer of Finite Depth
,”
Int. Commun. Heat Mass Transfer
,
31
, pp.
1
10
.10.1016/S0735-1933(03)00196-9
17.
Geng
,
P.
, and
Kuznetsov
,
A. V.
,
2004
, “
Effect of Small Solid Particles on the Development of Bioconvection Plumes
,”
Int. Commun. Heat Mass Transfer
,
31
, pp.
629
638
.10.1016/S0735-1933(04)00050-8
18.
Geng
,
P.
, and
Kuznetsov
,
A. V.
,
2005
, “
Settling of Bidispersed Small Solid Particles in a Dilute Suspension Containing Gyrotactic Micro-Organisms
,”
Int. J. Eng. Sci.
,
43
, pp.
992
1010
.10.1016/j.ijengsci.2005.03.002
19.
Geng
,
P.
, and
Kuznetsov
A. V.
,
2005
, “
Introducing the Concept of Effective Diffusivity to Evaluate the Effect of Bioconvection on Small Solid Particles
,”
Int. J. Transp. Phenom.
,
7
, pp.
321
338
.
20.
Kuznetsov
,
A. V.
,
2005
, “
The Onset of Bioconvection in a Suspension of Gyrotactic Microorganisms in a Fluid Layer of Finite Depth Heated From Below
,”
Int. Commun. Heat Mass Transfer
,
32
, pp.
574
582
.10.1016/j.icheatmasstransfer.2004.10.021
21.
Kuznetsov
,
A. V.
, and
Geng
,
P.
,
2005
, “
The Interaction of Bioconvection Caused by Gyrotactic Micro-Organisms and Settling of Small Solid Particles
,”
Int. J. Numer. Methods Heat Fluid Flow
,
15
, pp.
328
347
.10.1108/09615530510590597
22.
Kuznetsov
,
A. V.
,
2010
, “
The Onset of Nanofluid Bioconvection in a Suspension Containing Both Nanoparticles and Gyrotactic Microorganisms
,”
Int. Commun. Heat Mass Transfer
,
37
, pp.
1421
1425
.10.1016/j.icheatmasstransfer.2010.08.015
23.
Kuznetsov
,
A. V.
,
2011
, “
Non-Oscillatory and Oscillatory Nanofluid Bio-Thermal Convection in a Horizontal Layer of Finite Depth
,”
Eur. J. Mech. B/Fluids
,
30
, pp.
156
165
.10.1016/j.euromechflu.2010.10.007
24.
Kuznetsov
,
A. V.
,
2011
, “
Nanofluid Bioconvection in Water-Based Suspensions Containing Nanoparticles and Oxytactic Microorganisms: Oscillatory Instability
,”
Nanoscale Res. Lett.
,
6
,
p. 100
.10.1186/1556-276X-6-100
25.
Kuznetsov
,
A. V.
,
2005
, “
Thermo-Bioconvection in a Suspension of Oxytactic Bacteria
,”
Int. Commun. Heat Mass Transfer
,
32
, pp.
991
999
.10.1016/j.icheatmasstransfer.2004.11.005
26.
Kuznetsov
,
A. V.
,
2005
, “
Investigation of the Onset of Thermo-Bioconvection in a Suspension of Oxytactic Microorganisms in a Shallow Fluid Layer Heated From Below
,”
Theor. Comput. Fluid Dyn.
,
19
, pp.
287
299
.10.1007/s00162-005-0167-3
27.
Kuznetsov
,
A. V.
,
2006
, “
The Onset of Thermo-Bioconvection in a Shallow Fluid Saturated Porous Layer Heated From Below in a Suspension of Oxytactic Microorganisms
,”
Eur. J. Mech. B/Fluids
,
25
, pp.
223
233
.10.1016/j.euromechflu.2005.06.003
28.
Kuznetsov
,
A. V.
,
2011
, “
Bio-Thermal Convection Induced by Two Different Species of Microorganisms
,”
Int. Commun. Heat Mass Transfer
,
38
, pp.
548
553
.10.1016/j.icheatmasstransfer.2011.02.006
29.
Aziz
,
A.
,
Khan
,
W. A.
, and
Pop
,
I.
,
2012
, “
Free Convection Boundary Layer Flow Past a Horizontal Flat Plate Embedded in Porous Medium Filled by Nanofluid Containing Gyrotactic Microorganisms
,”
Int. J. Thermal Sci.
,
56
, pp.
48
57
.10.1016/j.ijthermalsci.2012.01.011
30.
Polyansky
,
O. P.
,
Reverdatto
,
V. V.
, and
Sverdlova
,
V. G.
,
2002
, “
Convection of Two-Phase Fluid in a Layered Porous Medium Driven by the Heat Of Magmatic Dikes and Sills
,”
Geochemistry Internat.
40
(
Suppl. 1
), pp.
S69
S81
.
31.
Stewart
,
T. L.
, and
Fogler
,
H. S.
,
2001
, “
Biomass Plug Development and Propagation in Porous Media
,”
Biotechnol. Bioeng.
,
72
, pp.
353
363
.10.1002/1097-0290(20010205)72:3<353::AID-BIT13>3.0.CO;2-U
32.
Kim
,
D.-S.
, and
Fogler
,
H. S.
,
2000
, “
Biomass Evolution in Porous Media and Its Effects on Permeability Under Starvation Conditions
,”
Biotechnol. Bioeng.
,
69
, pp.
47
56
.10.1002/(SICI)1097-0290(20000705)69:1<47::AID-BIT6>3.0.CO;2-N
33.
Kuznetsov
,
A. V.
,
2011
,
Emerging Topics in Heat and Mass Transfer in Porous Media: From Bioeengineering and Microelectronics to Nanotehnology
,
Springer
,
Houten, The Netherlands
.
34.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2010
, “
Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate
,”
Int. J. Thermal Sci.
,
49
, pp.
243
247
.10.1016/j.ijthermalsci.2009.07.015
35.
Ibrahim
,
W.
,
Shankar
,
B.
, and
Nandeppanavar
,
M. M.
,
2013
, “
MHD Stagnation Point Flow and Heat Transfer Due to Nanofluid Towards a Stretching Sheet
,”
Int. J. Heat and Mass Transfer
,
56
, pp.
1
9
.10.1016/j.ijheatmasstransfer.2012.08.034
36.
Fang
,
T.-G.
,
Zhang
,
J.
, and
Yao
,
S.-S.
,
2009
, “
Viscous Flow Over an Unsteady Shrinking Sheet With Mass Transfer
,”
Chin. Phys. Lett.
,
26
, pp.
014703
.10.1088/0256-307X/26/1/014703
37.
Bhattacharyya
,
K.
,
2011
, “
Boundary Layer Flow and Heat Transfer Over an Exponentially Shrinking Sheet
,”
Chin. Phys. Lett.
,
28
, p.
074701
.10.1088/0256-307X/28/7/074701
38.
Bhattacharyya
,
K.
, and
Vajravelu
,
K.
,
2012
, “
Stagnation-Point Flow and Heat Transfer Over an Exponentially Shrinking Sheet
,”
Commun. Nonlinear Sci. Numer. Simulat.
,
17
, pp.
2728
2734
.10.1016/j.cnsns.2011.11.011
39.
Bachok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2012
, “
Unsteady Boundary-Layer Flow and Heat Transfer of a Nanofluid Over a Permeable Stretching/Shrinking Sheet
,”
Int. J. Heat Mass Transfer
,
55
, pp.
2102
2109
.10.1016/j.ijheatmasstransfer.2011.12.013
40.
Bachok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2012
, “
The Boundary Layers of an Unsteady Stagnation-Point Flow in a Nanofluid
,”
Int. J. Heat Mass Transfer
,
55
, pp.
6499
6505
.10.1016/j.ijheatmasstransfer.2012.06.050
41.
Bachok
,
N.
,
Ishak
,
A.
, and
Pop
,
I.
,
2013
, “
Boundary Layer Stagnation-Point Flow Toward a Stretching/Shrinking Sheet in a Nanofluid
,”
ASME J. Heat Transfer
,
135
,
5
pages.10.1115/1.4023303
42.
Zaimi
,
K.
,
Ishak
,
A.
, and
Pop
,
I.
,
2012
, “
Boundary Layer Flow and Heat Transfer Past a Permeable Shrinking Sheet in a Nanofluid With Radiation Effect
,”
Adv. Mech. Eng.
,
7
pages. 10.1155/2012/340354
43.
Weidman
,
P. D.
,
Kubitschek
,
D. G.
, and
Davis
,
A. M. J.
,
2006
, “
The Effect of Transpiration on Self-Similar Boundary Layer Flow Over Moving Surfaces
,”
Int. J. Eng. Sci.
,
44
, pp.
730
737
.10.1016/j.ijengsci.2006.04.005
44.
Roşca
,
A. V.
, and
Pop
,
I.
,
2013
, “
Flow and Heat Transfer Over a Vertical Permeable Stretching/Shrinking Sheet With A Second Order Slip
,”
Int. J. Heat Mass Transfer
,
60
, pp.
355
364
.10.1016/j.ijheatmasstransfer.2012.12.028
You do not currently have access to this content.