This paper presents the motion of unsteady gravity-induced nanofluid flow containing gyrotactic micro-organisms along downward vertical convectively heated surface subject to passively controlled nanofluid. Considering the influence of temperature on the dynamic viscosity during convection and nature of thermal conductivity during heat conduction processes, these thermophysical properties are treated as linear functions of temperature. The governing equations are nondimensionalized by using suitable similarity transformation. The dimensionless nonlinear coupled PDEs are solved using a new pseudo-spectral technique called paired quasi-linearization method (PQLM). Convergence tests and residual error analysis are also presented to validate the accuracy, solution error, and computational convergence. The proposed PQLM yields accurate results which are obtained after a very few iterations. Minimum coefficients of (ξ/xRex)Shx with Sc are obtained at final steady stage.

References

References
1.
Choi
,
S. U. S.
, and
Eastman
,
J. A.
,
1995
, “
Enhancing Thermal Conductivity of Fluids With Nanoparticles
,”
ASME Publ. FED
,
231
, pp.
99
106
.
2.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
,
128
(
3
), pp.
240
250
.
3.
Animasaun
,
I. L.
,
2015
, “
Effects of Thermophoresis, Variable Viscosity and Thermal Conductivity on Free Convective Heat and Mass Transfer of Non-Darcian MHD Dissipative Casson Fluid Flow With Suction and nth Order of Chemical Reaction
,”
J. Niger. Math. Soc.
,
34
(
1
), pp.
11
31
.
4.
Animasaun
,
I. L.
,
2016
, “
47 nm Alumina–Water Nanofluid Flow Within Boundary Layer Formed on Upper Horizontal Surface of Paraboloid of Revolution in the Presence of Quartic Autocatalysis Chemical Reaction
,”
Alexandria Eng. J.
, (in press).
5.
Makinde
,
O. D.
, and
Animasaun
,
I. L.
,
2016
, “
Thermophoresis and Brownian Motion Effects on MHD Bioconvection of Nanofluid With Nonlinear Thermal Radiation and Quartic Chemical Reaction Past an Upper Horizontal Surface of a Paraboloid of Revolution
,”
J. Mol. Liq.
,
221
, pp.
733
743
.
6.
Kuznetsov
,
A.
, and
Nield
,
D.
,
2010
, “
Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate
,”
Int. J. Therm. Sci.
,
49
(
2
), pp.
243
247
.
7.
Khan
,
W.
, and
Makinde
,
O.
,
2014
, “
MHD Nanofluid Bioconvection Due to Gyrotactic Microorganisms Over a Convectively Heat Stretching Sheet
,”
Int. J. Therm. Sci.
,
81
, pp.
118
124
.
8.
Kuznetsov
,
A.
, and
Avramenko
,
A.
,
2004
, “
Effect of Small Particles on This Stability of Bioconvection in a Suspension of Gyrotactic Microorganisms in a Layer of Finite Depth
,”
Int. Commun. Heat Mass Transfer
,
31
(
1
), pp.
1
10
.
9.
Kuznetsov
,
A.
,
2010
, “
The Onset of Nanofluid Bioconvection in a Suspension Containing Both Nanoparticles and Gyrotactic Microorganisms
,”
Int. Commun. Heat Mass Transfer
,
37
(
10
), pp.
1421
1425
.
10.
Stokes
,
G. G.
,
1851
,
On the Effect of the Internal Friction of Fluids on the Motion of Pendulums
, Vol.
9
,
Pitt Press
, Pittsburgh, PA.
11.
Dennis
,
S.
,
1972
, “
The Motion of a Viscous Fluid Past an Impulsively Started Semi-Infinite Flat Plate
,”
IMA J. Appl. Math.
,
10
(
1
), pp.
105
117
.
12.
Watkins
,
C.
,
1975
, “
Heat Transfer in the Laminar Boundary Layer Over an Impulsively Started Flat Plate
,”
ASME J. Heat Transfer
,
97
(
3
), pp.
482
484
.
13.
Williams
,
J. C.
, and
Rhyne
,
T. H.
,
1980
, “
Boundary Layer Development on a Wedge Impulsively Set Into Motion
,”
SIAM J. Appl. Math.
,
38
(
2
), pp.
215
224
.
14.
Liao
,
S.
,
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
.
15.
Nazar
,
R.
,
Amin
,
N.
, and
Pop
,
I.
,
2004
, “
Unsteady Boundary Layer Flow Due to a Stretching Surface in a Rotating Fluid
,”
Mech. Res. Commun.
,
31
(
1
), pp.
121
128
.
16.
Motsa
,
S.
,
Sibanda
,
P.
, and
Shateyi
,
S.
,
2010
, “
A New Spectral-Homotopy Analysis Method for Solving a Nonlinear Second Order BVP
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
9
), pp.
2293
2302
.
17.
Motsa
,
S. S.
,
2014
, “
On the Practical Use of the Spectral Homotopy Analysis Method and Local Linearisation Method for Unsteady Boundary-Layer Flows Caused by an Impulsively Stretching Plate
,”
Numer. Algorithms
,
66
(
4
), pp.
865
883
.
18.
Motsa
,
S. S.
, and
Animasaun
,
I. L.
,
2015
, “
A New Numerical Investigation of Some Thermo-Physical Properties on Unsteady MHD Non-Darcian Flow Past an Impulsively Started Vertical Surface
,”
Therm. Sci.
,
19
(Suppl. 1), pp.
S249
S258
.
19.
Animasaun
,
I. L.
,
2016
, “
Double Diffusive Unsteady Convective Micropolar Flow Past a Vertical Porous Plate Moving Through Binary Mixture Using Modified Boussinesq Approximation
,”
Ain Shams Eng. J.
,
7
(
2
), pp.
755
765
.
20.
Animasaun
,
I. L.
,
2015
, “
Dynamics of Unsteady MHD Convective Flow With Thermophoresis of Particles and Variable Thermo-Physical Properties Past a Vertical Surface Moving Through Binary Mixture
,”
Open J. Fluid Dyn.
,
5
(
2
), pp.
106
120
.
21.
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
.
22.
Omowaye
,
A. J.
, and
Animasaun
,
I. L.
,
2016
, “
Upper-Convected Maxwell Fluid Flow With Variable Thermo-Physical Properties Over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification
,”
J. Appl. Fluid Mech.
,
9
(
4
), pp.
1777
1790
.
23.
Thomas
,
S.
, and
Sobhan
,
C. B. P.
,
2011
, “
A Review of Experimental Investigations on Thermal Phenomena in Nanofluids
,”
Nanoscale Res. Lett.
,
6
(
1
), p. 377.
24.
Vajravelu
,
K.
,
Prasad
,
K. V.
, and
Chiu-On
,
N.
,
2013
, “
The Effect of Variable Viscosity on the Flow and Heat Transfer of a Viscous Ag-Water and Cu-Water Nanofluids
,”
J. Hydrodyn., Ser. B
,
25
(
1
), pp.
1
9
.
25.
Noghrehabadi
,
A.
,
Ghalambaz
,
M.
, and
Ghanbarzadeh
,
A.
,
2014
, “
Effects of Variable Viscosity and Thermal Conductivity on Natural-Convection of Nanofluids Past a Vertical Plate in Porous Media
,”
J. Mech.
,
30
(
3
), pp.
265
275
.
26.
Raees
,
A.
,
Xu
,
H.
,
Sun
,
Q.
, and
Pop
,
I.
,
2015
, “
Mixed Convection in Gravity-Driven Nano-Liquid Film Containing Both Nanoparticles and Gyrotactic Microorganisms
,”
Appl. Math. Mech.
,
36
(
2
), pp.
163
178
.
27.
Batchelor
,
G. K.
,
2000
,
An Introduction to Fluid Dynamics
,
Cambridge University Press
, New York.
28.
Charraudeau
,
J.
,
1975
, “
Influence de gradients de proprietes physiques en convection forcee-application au cas du tube
,”
Int. J. Heat Mass Transfer
,
18
(
1
), pp.
87
95
.
29.
Canuto
,
C.
,
Hussaini
,
M. Y.
,
Quarteroni
,
A. M.
, and
Thomas
,
A.
, Jr.
,
2012
,
Spectral Methods in Fluid Dynamics
,
Springer Science & Business Media
, Heidelberg, Germany.
30.
Trefethen
,
L. N.
,
2000
,
Spectral Methods in MATLAB
, Vol.
10
,
SIAM
, Philadelphia, PA.
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