The natural convection fluid flow and heat transfer in an annulus of two differentially heated confocal elliptic cylinders filled with the Cu–water nanofluid are investigated numerically. The outer cylinder is maintained at a constant temperature Tc while the inner cylinder is kept at a differentially higher constant temperature Th. Equations of continuity, momentum, and energy are formulated using the dimensionless form in elliptic coordinates for two-dimensional steady, laminar, and incompressible flow, which is expressed in terms of stream function, vorticity, and temperature. The basic equations are discretized using the finite-volume method. Using a developed code, calculations were performed for Rayleigh number (103 ≤ Ra ≤ 3 × 105), volume fraction of nanoparticles (0 ≤ ϕ  ≤ 0.12), and eccentricity of the inner ellipse, ε1 = 0.7, 0.8, and 0.9. The eccentricity of outer ellipse and the angle of orientation are fixed at 0.6 deg and 0 deg, respectively. Results are presented in the form of stream lines, isotherm plots, and local and average Nusselt numbers. The results discussed in this present work show the existence of a very good agreement between the present results and those from the previous researches.

References

References
1.
Godson
,
L.
,
Raja
,
B.
,
Mohan Lal
,
D.
, and
Wongwises
,
S.
,
2010
, “
Enhancement of Heat Transfer Using Nanofluids—An Overview
,”
Renewable Sustainable Energy Rev.
,
14
(
2
), pp.
629
641
.
2.
Kang
,
H. U.
,
Kim
,
S. H.
, and
Oh
,
J. M.
,
2006
, “
Estimation of Thermal Conductivity of Nanofluid Using Experimental Effective Particle Volume
,”
Exp. Heat Transfer
,
19
(
3
), pp.
181
191
.
3.
Velagapudi
,
V.
,
Konijeti
,
K. R.
, and
Aduru
,
K. S. C.
,
2008
, “
Empirical Correlations to Predict Thermophysical and Heat Transfer Characteristics of Nanofluids
,”
Therm. Sci.
,
12
(
2
), pp.
27
37
.
4.
Turgut
,
A.
,
Tavman
,
I.
,
Chirtoc
,
M.
,
Schuchmann
,
H.
,
Sauter
,
C.
, and
Tavman
,
S.
,
2009
, “
Thermal Conductivity and Viscosity Measurements of Water-Based TiO2 Nanofluids
,”
Int. J. Thermophys.
,
30
(
4
), pp.
1213
1226
.
5.
Rudyak
,
V. Y.
,
Belkin
,
A.
, and
Tomilina
,
E.
,
2010
, “
On the Thermal Conductivity of Nanofluids
,”
Tech. Phys. Lett.
,
36
(
7
), pp.
660
662
.
6.
Murugesan
,
C.
, and
Sivan
,
S.
,
2010
, “
Limits for Thermal Conductivity of Nanofluids
,”
Therm. Sci.
,
14
(
1
), pp.
65
71
.
7.
Nayak
,
A.
,
Singh
,
R.
, and
Kulkarni
,
P.
,
2010
, “
Measurement of Volumetric Thermal Expansion Coefficient of Various Nanofluids
,”
Tech. Phys. Lett.
,
36
(
8
), pp.
696
698
.
8.
Khanafer
,
K.
,
Vafai
,
K.
, and
Lightstone
,
M.
,
2003
, “
Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids
,”
Int. J. Heat Mass Transfer.
,
46
(
19
), pp.
3639
3653
.
9.
Jou
,
R.-Y.
, and
Tzeng
,
S.-C.
,
2006
, “
Numerical Research of Nature Convective Heat Transfer Enhancement Filled With Nanofluids in Rectangular Enclosures
,”
Int. Commun. Heat Mass Transfer.
,
33
(
6
), pp.
727
736
.
10.
Abu-Nada
,
E.
, and
Chamkha
,
A. J.
,
2010
, “
Mixed Convection Flow in a Lid-Driven Inclined Square Enclosure Filled With a Nanofluid
,”
Eur. J. Mech.-B/Fluids
,
29
(
6
), pp.
472
482
.
11.
Abu-Nada
,
E.
, and
Chamkha
,
A. J.
,
2010
, “
Effect of Nanofluid Variable Properties on Natural Convection in Enclosures Filled With an CuO-EG-Water Nanofluid
,”
Int. J. Therm. Sci.
,
49
(
12
), pp.
2339
2352
.
12.
Basak
,
T.
, and
Chamkha
,
A. J.
,
2012
, “
Heatline Analysis on Natural Convection for Nanofluids Confined Within Square Cavities With Various Thermal Boundary Conditions
,”
Int. J. Heat Mass Transfer
,
55
(
21–22)
, pp.
5526
5543
.
13.
Chamkha
,
A. J.
, and
Abu-Nada
,
E.
,
2012
, “
Mixed Convection Flow in Single- and Double-Lid Driven Square Cavities Filled With Water–Al2O3 Nanofluid: Effect of Viscosity Models
,”
Eur. J. Mech.-B/Fluids
,
36
, pp.
82
96
.
14.
Chamkha
,
A. J.
, and
Ismael
,
M. A.
,
2013
, “
Conjugate Heat Transfer in a Porous Cavity Filled With Nanofluids and Heated by Triangular Thick Wall
,”
Int. J. Therm. Sci.
,
67
, pp.
135
151
.
15.
Tayebi
,
T.
,
Djezzar
,
M.
, and
Saadaoui
,
K.
,
2013
, “
Effect of Sinusoidal Thermal Boundary Condition on Natural Convection in a Cavity Filled With Cu–Water Nanofluid
,”
J. Nanofluids
,
2
(
2
), pp.
120
126
.
16.
Tayebi
,
T.
, and
Saadaoui
,
K.
,
2013
, “
Enhancement of Heat Transfer in a Cavity Filled With Cu–Water Nanofluid
,”
International Symposium on Materials and Sustainable Development
, pp.
122
127
.
17.
Mansour
,
M. A.
,
Bakeir
,
M. A. Y.
, and
Chamkha
,
A. J.
,
2014
, “
Numerical Modeling of Natural Convection of a Nanofluid Between Two Enclosures
,”
J. Nanofluids
,
3
(
4
), pp.
368
379
.
18.
Chamkha
,
A. J.
, and
Ismael
,
M. A.
,
2014
, “
Natural Convection in Differentially Heated Partially Porous Layered Cavities Filled With a Nanofluid
,”
Numer. Heat Transfer, Part A
,
65
(
11
), pp.
1089
1113
.
19.
Garoosi
,
F.
,
Jahanshaloo
,
L.
,
Rashidi
,
M. M.
,
Badakhsh
,
A.
, and
Ali
,
M. E.
,
2015
, “
Numerical Simulation of Natural Convection of the Nanofluid in Heat Exchangers Using a Buongiorno Model
,”
Appl. Math. Comput.
,
254
, pp.
183
203
.
20.
Sheikholeslami
,
M.
, and
Ellahi
,
R.
,
2015
, “
Three Dimensional Mesoscopic Simulation of Magnetic Field Effect on Natural Convection of Nanofluid
,”
Int. J. Heat Mass Transfer
,
89
, pp.
799
808
.
21.
Tayebi
,
T.
, and
Djezzar
,
M.
,
2015
, “
Numerical Study of Natural Convection Flow in a Square Cavity With Linearly Heating on Bottom Wall Using Copper–Water Nanofluid
,”
J. Nanofluids
,
4
(
1
), pp.
120
126
.
22.
Sheikholeslami
,
M.
,
Hayat
,
T.
, and
Alsaedi
,
A.
,
2016
, “
MHD Free Convection of Al2O3–Water Nanofluid Considering Thermal Radiation: A Numerical Study
,”
Int. J. Heat Mass Transfer
,
96
, pp.
513
524
.
23.
Togun
,
H.
,
Abdulrazzaq
,
T.
,
Kazi
,
S.
,
Badarudin
,
A.
,
Kadhum
,
A.
, and
Sadeghinezhad
,
E.
,
2014
, “
A Review of Studies on Forced, Natural and Mixed Heat Transfer to Fluid and Nanofluid Flow in an Annular Passage
,”
Renewable Sustainable Energy Rev.
,
39
, pp.
835
856
.
24.
Parvin
,
S.
,
Nasrin
,
R.
,
Alim
,
M.
,
Hossain
,
N.
, and
Chamkha
,
A. J.
,
2012
, “
Thermal Conductivity Variation on Natural Convection Flow of Water–Alumina Nanofluid in an Annulus
,”
Int. J. Heat Mass Transfer
,
55
(
19–20
), pp.
5268
5274
.
25.
Nasrin
,
R.
,
Alim
,
M. A.
, and
Chamkha
,
A. J.
,
2012
, “
Effect of Viscosity Variation on Natural Convection Flow of Water–Alumina Nanofluid in an Annulus With Internal Heat Generation
,”
Heat Transfer—Asian Res.
,
41
(
6
), pp.
536
552
.
26.
Habibi Matin
,
M.
, and
Pop
,
I.
,
2013
, “
Natural Convection Flow and Heat Transfer in an Eccentric Annulus Filled by Copper Nanofluid
,”
Int. J. Heat Mass Transfer
,
61
, pp.
353
364
.
27.
Mehrizi
,
A. A.
,
Farhadi
,
M.
, and
Shayamehr
,
S.
,
2013
, “
Natural Convection Flow of Cu–Water Nanofluid in Horizontal Cylindrical Annuli With Inner Triangular Cylinder Using Lattice Boltzmann Method
,”
Int. Commun. Heat Mass Transfer
,
44
, pp.
147
156
.
28.
Izadi
,
M.
,
Shahmardan
,
M.
, and
Behzadmehr
,
A.
,
2013
, “
Richardson Number Ratio Effect on Laminar Mixed Convection of a Nanofluid Flow in an Annulus
,”
Int. J. Comput. Methods Eng. Sci. Mech.
,
14
(
4
), pp.
304
316
.
29.
Sheikholeslami
,
M.
,
Gorji-Bandpy
,
M.
, and
Ganji
,
D. D.
,
2014
, “
MHD Free Convection in an Eccentric Semi-Annulus Filled With Nanofluid
,”
J. Taiwan Inst. Chem. Eng.
,
45
(
4
), pp.
1204
1216
.
30.
Kandelousi
,
M. S.
,
2014
, “
Effect of Spatially Variable Magnetic Field on Ferrofluid Flow and Heat Transfer Considering Constant Heat Flux Boundary Condition
,”
Eur. Phys. J. Plus
,
129
, p.
248
.
31.
Seyyedi
,
S.
,
Dayyan
,
M.
,
Soleimani
,
S.
, and
Ghasemi
,
E.
,
2014
, “
Natural Convection Heat Transfer Under Constant Heat Flux Wall in a Nanofluid Filled Annulus Enclosure
,”
Ain Shams Eng. J.
,
6
(
1
), pp.
267
280
.
32.
Arbaban
,
M.
, and
Salimpour
,
M.
,
2015
, “
Enhancement of Laminar Natural Convective Heat Transfer in Concentric Annuli With Radial Fins Using Nanofluids
,”
Heat Mass Transfer
,
51
(
3
), pp.
353
362
.
33.
Moghari
,
R. M.
,
Talebi
,
F.
,
Rafee
,
R.
, and
Shariat
,
M.
,
2014
, “
Numerical Study of Pressure Drop and Thermal Characteristics of Al2O3–Water Nanofluid Flow in Horizontal Annuli
,”
Heat Transfer Eng.
,
36
(
2
), pp.
166
177
.
34.
Lee
,
J. H.
, and
Lee
,
T. S.
,
1981
, “
Natural Convection in the Annuli Between Horizontal Confocal Elliptic Cylinders
,”
Int. J. Heat Mass Transfer
,
24
, pp.
1739
1742
.
35.
Schreiber
,
W. C.
, and
Singh
,
S. N.
,
1985
, “
Natural Convection Between Confocal Horizontal Elliptical Cylinders
,”
Int. J. Heat Transfer
,
28
(
4
), pp.
807
822
.
36.
Elshamy
,
M. M.
,
Ozisik
,
M. N.
, and
Coulter
,
J. P.
,
1990
, “
Correlation for Laminar Natural Convection Between Confocal Horizontal Elliptical Cylinders
,”
Numer. Heat Transfer, Part A
,
18
(
1
), pp.
95
112
.
37.
Cheng
,
C.-H.
, and
Chao
,
C.-C.
,
1996
, “
Numerical Prediction of the Buoyancy-Driven Flow in the Annulus Between Horizontal Eccentric Elliptical Cylinders
,”
Numer. Heat Transfer, Part A
,
30
(
3
), pp.
283
303
.
38.
Mota
,
J. P. B.
,
Esteves
,
I. A. A. C.
,
Portugal
,
C. A. M.
,
Esperanca
,
J. M. S. S.
, and
Saatdjian
,
E.
,
2000
, “
Natural Convection Heat Transfer in Horizontal Eccentric Elliptic Annuli Containing Saturated Porous Media
,”
Int. J. Heat Mass Transfer
,
43
(
24
), pp.
4367
4379
.
39.
Hirose
,
K.
,
Hachinohe
,
T.
, and
Ishii
,
Y.
,
2001
, “
Natural Convection Heat Transfer in Eccentric Horizontal Annuli Between a Heated Outer Tube and a Cooled Inner Tube With Different Orientation: The Case of an Elliptical Outer Tube
,”
Heat Transfer—Asian Res.
,
30
(
8
), pp.
624
635
.
40.
Zerari
,
K.
,
Afrid
,
M.
, and
Groulx
,
D.
,
2013
, “
Forced and Mixed Convection in the Annulus Between Two Horizontal Confocal Elliptical Cylinders
,”
Int. J. Therm. Sci.
,
74
, pp.
126
144
.
41.
Bouras
,
A.
,
Djezzar
,
M.
,
Naji
,
H.
, and
Ghernoug
,
C.
,
2014
, “
Numerical Computation of Double-Diffusive Natural Convective Flow Within an Elliptic-Shape Enclosure
,”
Int. Commun. Heat Mass Transfer
,
57
, pp.
183
192
.
42.
Izadi
,
M.
,
Behzadmehr
,
A.
, and
Jalali-Vahida
,
D.
,
2009
, “
Numerical Study of Developing Laminar Forced Convection of a Nanofluid in an Annulus
,”
Int. J. Therm. Sci.
,
48
(
11
), pp.
2119
2129
.
43.
Dawood
,
H.
,
Mohammed
,
H.
, and
Munisamy
,
K.
,
2014
, “
Heat Transfer Augmentation Using Nanofluids in an Elliptic Annulus With Constant Heat Flux Boundary Condition
,”
Case Stud. Therm. Eng.
,
4
, pp.
32
41
.
44.
Moon
,
P.
, and
Spencer
,
D. E.
,
1971
,
Field Theory Handbook
,
Springer-Verlag
,
New York
.
45.
Patankar
,
S.
,
1980
,
Numerical Heat Transfer and Fluid Flow
,
CRC Press
,
Boca Raton, FL
.
46.
Nogotov
,
F.
,
1978
, “
Applications of Numerical Heat Transfer
,” NASA, Washington, DC, NASA STI/Recon Technical Report A, Report No. 7914672.
47.
Brinkman
,
H.
,
1952
, “
The Viscosity of Concentrated Suspensions and Solutions
,”
J. Chem. Phys.
,
20
(
4
), pp.
571
571
.
48.
Maxwell
,
C.
,
1881
,
A Treatise on Electricity and Magnetism
,
Clarendon Press
,
Oxford, UK
.
49.
Mahmoodi
,
M.
,
2011
, “
Numerical Simulation of Free Convection of Nanofluid in a Square Cavity With an Inside Heater
,”
Int. J. Therm. Sci.
,
50
(
11
), pp.
2161
2175
.
50.
Abu-Nada
,
E.
,
Masoud
,
Z.
, and
Hijazi
,
A.
,
2008
, “
Natural Convection Heat Transfer Enhancement in Horizontal Concentric Annuli Using Nanofluids
,”
Int. Commun. Heat Mass Transfer
,
35
(
5
), pp.
657
665
.
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