This paper reports the numerical results for the natural convection flow of a two-phase dusty nanofluid along a vertical wavy frustum of a cone. The general governing equations are transformed into parabolic partial differential equations, which are then solved numerically with the help of implicit finite difference method. Comprehensive flow formations of carrier and dusty phases are given with the aim to predict the behavior of heat and mass transport across the heated wavy frustum of a cone. The effectiveness of utilizing the nanofluids to control skin friction and heat and mass transport is analyzed. The results clearly show that the shape of the waviness changes when nanofluid is considered. It is shown that the modified diffusivity ratio parameter, NA, extensively promotes rate of mass transfer near the vicinity of the cone, whereas heat transfer rate reduces.

References

1.
Choi
,
S. U. S.
,
1995
, “
Enhancing Thermal Conductivity of Fluids With Nanoparticles
,”
Development and Applications of Non-Newtonian Flows
,
D. A.
Siginer
, and
H. P.
Wang
, eds.,
ASME
,
New York
, pp.
99
105
.
2.
Xuan
,
Y.
, and
Li
,
Q.
,
2000
, “
Heat Transfer Enhancement of Nanofluids
,”
Int. J. Heat Transfer Fluid Flow
,
21
(
1
), pp.
58
64
.
3.
Nnanna
,
A. G.
,
2007
, “
Experimental Model of Temperature-Driven Nanofluids
,”
ASME J. Heat Transfer
,
129
(
6
), pp.
697
704
.
4.
Mintsa
,
H. A.
,
Roy
,
G.
,
Nguyen
,
C. T.
, and
Doucet
,
D.
,
2009
, “
New Temperature Dependent Thermal Conductivity Data for Water-Based Nanofluids
,”
Int. J. Therm. Sci.
,
48
(
2
), pp.
363
371
.
5.
Gu
,
B.
,
Hou
,
B.
,
Lu
,
Z.
,
Wang
,
Z.
, and
Chen
,
S.
,
2013
, “
Thermal Conductivity of Nanofluids Containing High Aspect Ratio Fillers
,”
Int. J. Heat Mass Transfer
,
64
, pp.
108
114
.
6.
Sundar
,
L. S.
,
Farooky
,
M. H.
,
Sarada
,
S. N.
, and
Singh
,
M. K.
,
2013
, “
Experimental Thermal Conductivity of Ethylene Glycol and Water Mixture Based Low Volume Concentration of Al2O3 and CuO Nanofluids
,”
Int. Commun. Heat Mass Transfer
,
41
, pp.
41
46
.
7.
Lomascolo
,
M.
,
Colangelo
,
G.
,
Milanese
,
M.
, and
Risi
,
A. D.
,
2015
, “
Review of Heat Transfer in Nanofluids: Conductive, Convective and Radiative Experimental Results
,”
Renewable Sustainable Energy Rev.
,
43
, pp.
1182
1198
.
8.
Colangelo
,
G.
,
Favale
,
E.
,
Risi
,
A. D.
, and
Laforgia
,
D.
,
2012
, “
Results of Experimental Investigations on the Heat Conductivity of Nanofluids Based on Diathermic Oil for High Temperature Applications
,”
Appl. Energy
,
97
, pp.
828
833
.
9.
Colangelo
,
G.
,
Favale
,
E.
,
Miglietta
,
P.
,
Milanese
,
M.
, and
Risi
,
A. D.
,
2016
, “
Thermal Conductivity, Viscosity and Stability of Al2O3-Diathermic Oil Nanofluids for Solar Energy Systems
,”
Energy
,
95
, pp.
124
136
.
10.
Rudinger
,
G.
,
1980
,
Fundamentals of Gas-Particle Flow
,
Elsevier
,
Amsterdam, The Netherlands
.
11.
Farbar
,
L.
, and
Morley
,
M. J.
,
1957
, “
Heat Transfer to Flowing Gas-Solid Mixtures in a Circular Tube
,”
Ind. Eng. Chem.
,
49
(
7
), pp.
1143
1150
.
12.
Saffman
,
P. G.
,
1962
, “
On the Stability of Laminar Flow of a Dusty Gas
,”
J. Fluid Mech.
,
13
(
01
), pp.
120
128
.
13.
Marble
,
F. E.
,
1963
, “
Dynamics of a Gas Containing Small Solid Particles
,”
Combustion and Propulsion, 5th AGARD Colloquium
,
Pergamon Press
,
Oxford, UK
.http://authors.library.caltech.edu/22071/1/147_Marble_FE_1963.pdf
14.
Singleton
,
R. E.
,
1964
, “
Fluid Mechanics of Gas-Solid Particle Flow in Boundary Layers
,” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
15.
Michael
,
D. H.
, and
Miller
,
D. A.
,
1966
, “
Plane Parallel Flow of a Dusty Gas
,”
Mathematica
,
13
(
1
), pp.
97
109
.
16.
Michael
,
D. H.
,
1968
, “
The Steady Motion of a Sphere in a Dusty Gas
,”
J. Fluid Mech.
,
31
(
01
), pp.
175
192
.
17.
Datta
,
N.
, and
Mishra
,
S. K.
,
1982
, “
Boundary Layer Flow of a Dusty Fluid Over a Semi-Infinite Flat Plate
,”
Acta Mech.
,
42
, pp.
71
83
.
18.
Gireesha
,
B. J.
,
Bagewadi
,
C. S.
, and
Kumara
,
B. C. P.
,
2009
, “
Pulsatile Flow of an Unsteady Dusty Fluid Through Rectangular Channel
,”
Commun. Nonlinear Sci. Numer. Simul.
,
14
(
5
), pp.
2103
2110
.
19.
Gireesha
,
B. J.
,
Bagewadi
,
C. S.
, and
Kumara
,
B. C. P.
,
2007
, “
Flow of Unsteady Dusty Fluid Under Varying Pulsatile Pressure Gradient in Anholonomic Co-Ordinate System
,”
Electron. J. Theor. Phys.
,
4
(
14
), pp.
9
16
.http://ejtp.com/articles/ejtpv4i14p9.pdf
20.
Siddiqa
,
S.
,
Hossain
,
M. A.
, and
Saha
,
S. C.
,
2015
, “
Two-Phase Natural Convection Flow of a Dusty Fluid
,”
Int. J. Numer. Method
,
25
(
7
), pp.
1542
1556
.
21.
Yao
,
L. S.
,
1983
, “
Natural Convection Along a Vertical Wavy Surface
,”
ASME J. Heat Transfer
,
105
(
3
), pp.
465
468
.
22.
Moulic
,
S. G.
, and
Yao
,
L. S.
,
1989
, “
Natural Convection Along a Wavy Surface With Uniform Heat Flux
,”
ASME J. Heat Transfer
,
111
(
4
), pp.
1106
1108
.
23.
Rees
,
D. A. S.
, and
Pop
,
I.
,
1995
, “
Free Convection Induced by a Vertical Wavy Surface With Uniform Heat Flux in a Porous Medium
,”
ASME J. Heat Transfer
,
117
(
2
), pp.
545
550
.
24.
Siddiqa
,
S.
,
Hossain
,
M. A.
, and
Saha
,
S. C.
,
2013
, “
Natural Convection Flow With Surface Radiation Along a Vertical Wavy Surface
,”
Numer. Heat Transfer, Part A
,
64
(
5
), pp.
400
415
.
25.
Pop
,
I.
, and
Na
,
T. Y.
,
1995
, “
Natural Convection From a Wavy Cone
,”
Appl. Sci. Res.
,
54
(
2
), pp.
125
136
.
26.
Na
,
T. Y.
, and
Chiou
,
J. P.
,
1979
, “
Laminar Natural Convection Over a Frustum of a Cone
,”
Appl. Sci. Res.
,
35
, pp.
409
421
.
27.
Pop
,
I.
, and
Na
,
T. Y.
,
1999
, “
Natural Convection Over a Vertical Wavy Frustum of a Cone
,”
J. Nonlinear Mech.
,
34
(
5
), pp.
925
934
.
28.
Siddiqa
,
S.
,
Begum
,
N.
, and
Hossain
,
M. A.
,
2016
, “
Radiation Effects From an Isothermal Vertical Wavy Cone With Variable Fluid Properties
,”
Appl. Math. Comput.
,
289
, pp.
149
158
.
29.
Siddiqa
,
S.
,
Hina
,
G.
,
Begum
,
N.
,
Saleem
,
S.
,
Hossain
,
M. A.
, and
Gorla
,
R. S. R.
,
2016
, “
Numerical and Analytical Solution of Nanofluid Bioconvection Due to Gyrotactic Microorganisms Along a Vertical Wavy Cone
,”
Int. J. Heat Mass Transfer
,
101
, pp.
608
613
.
30.
Siddiqa
,
S.
,
Begum
,
N.
,
Hossain
,
M. A.
, and
Massarotti
,
N.
,
2016
, “
Influence of Thermal Radiation on Contaminated Air and Water Flow Past a Vertical Wavy Frustum of a Cone
,”
Int. Commun. Heat Mass Transfer
,
76
, pp.
63
68
.
31.
Apazidis
,
N.
,
1990
, “
Temperature Distribution and Heat Transfer in a Particle-Fluid Flow Past a Heated Horizontal Plate
,”
Int. J. Multiphase Flow
,
16
(
3
), pp.
495
513
.
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