Owing to the rapid development of a number of technological and industrial sectors, high-performance electronic devices are now ubiquitous in modern engineering and industrial applications. Effective heat management is crucial to the smooth operation of such devices, and sometimes conventional methods of heat transfer fail to deliver the required performance. Recent advances in the field of nanofluids are a promising route to improve heat-transfer performance, and this is our motivation. We propose two computational fluid dynamics models for a rotor-stator cavity operating at Reω = 1.0 × 105 and filled with a fluid that consists of different volume fractions of Al2O3 nanoparticles. The first model simulates the nanofluid mixture using a single-phase transport model, and the second approach uses a two-phase transport model that allows for the relative velocity between the particle and fluid phases. All simulations are conducted using the second-order accurate solver, OpenFOAM®, that is based on the finite volume method and using Large eddy simulation methods. Our results show that the higher volume fractions of Al2O3 nanoparticles can achieve higher heat transfer rates, and at the same time, dilute nanoparticle concentrations have subtle effects on the momentum transport of the system. This is an advantage over micro-particle dispersion. Furthermore, we consider the effects of particle forces in the two-phase model, such as Brownian and thermophoresis forces, and suggest that the thermophoresis forces are the dominant effect within the cavity geometry.

1.
E.
Serre
,
P.
Bontoux
, and
B.
Launder
, “
Transitional-turbulent flow with heat transfer in a closed rotor-stator cavity
,”
J. Turbul.
5
,
1
3
(
2004
).
2.
S.
Poncet
and
E.
Serre
, “
Large eddy simulation of non-isothermal turbulent rotor-stator flows
,” in
The Twelfth International Symposium on Transport Phenomena and Dynamics of Rotating Machinery
,
2008
.
3.
E.
Tuliszka-Sznitko
,
A.
Zielinski
, and
W.
Majchrowski
, “
LES of the non-isothermal transitional flow in rotating cavity
,”
Int. J. Heat Fluid Flow
30
,
534
548
(
2009
).
4.
E.
Tuliszka-Sznitko
and
W.
Majchrowski
, “
LES and DNS of the flow with heat transfer in rotating cavity
,”
Comput. Methods Sci. Technol.
16
,
105
114
(
2010
).
5.
E.
Tuliszka-Sznitko
,
W.
Majchrowski
, and
K.
Kiełczewski
, “
Investigation of transitional and turbulent heat and momentum transport in a rotating cavity
,”
Int. J. Heat Fluid Flow
35
,
52
60
(
2012
).
6.
T. V.
Kármán
, “
Über laminare und turbulente reibung
,”
ZAMM- J. Appl. Math. Mech./Z. Angew. Math. Mech.
1
,
233
252
(
1921
).
7.
K.
Millsaps
, “
Heat transfer by laminar flow from a rotating plate
,”
J. Aeronaut. Sci.
18
,
354
355
(
1951
).
8.
E.
Cobb
and
O.
Saunders
, “
Heat transfer from a rotating disk
,”
Proc. R. Soc. A
236
,
343
351
(
1956
).
9.
N.
Nikitenko
, “
Experimental investigation of heat exchange of a disk and a screen
,”
J. Eng. Phys.
6
,
1
11
(
1963
).
10.
J.
Owen
,
C.
Haynes
, and
F.
Bayley
, “
Heat transfer from an air-cooled rotating disk
,”
Proc. R. Soc. A
336
,
453
473
(
1974
).
11.
J. W.
Daily
and
R. E.
Nece
, “
Chamber dimension effects on induced flow and frictional resistance of enclosed rotating disks
,”
J. Basic Eng.
82
,
217
230
(
1960
).
12.
J. M.
Owen
and
R. H.
Rogers
,
Flow and Heat Transfer in Rotating-Disc Systems
(
Research Studies Press
,
1989
).
13.
J.
Owen
and
R. H.
Rogers
,
Flow and Heat Transfer in Rotating Disc Systems, Volume 2: Rotating Cavities
(
Research Studies Press
,
1995
).
14.
A. J.
Faller
, “
Instability and transition of disturbed flow over a rotating disk
,”
J. Fluid Mech.
230
,
245
269
(
1991
).
15.
M.
Itoh
,
Y.
Yamada
,
S.
Imao
, and
M.
Gonda
, “
Experiments on turbulent flow due to an enclosed rotating disk
,”
Exp. Therm. Fluid Sci.
5
,
359
368
(
1992
).
16.
H. S.
Littell
and
J. K.
Eaton
, “
Turbulence characteristics of the boundary layer on a rotating disk
,”
J. Fluid Mech.
266
,
175
207
(
1994
).
17.
R.
Lingwood
, “
An experimental study of absolute instability of the rotating-disk boundary-layer flow
,”
J. Fluid Mech.
314
,
373
405
(
1996
).
18.
R. J.
Lingwood
, “
Absolute instability of the Ekman layer and related rotating flows
,”
J. Fluid Mech.
331
,
405
428
(
1997
).
19.
G.
Gauthier
,
P.
Gondret
, and
M.
Rabaud
, “
Axisymmetric propagating vortices in the flow between a stationary and a rotating disk enclosed by a cylinder
,”
J. Fluid Mech.
386
,
105
126
(
1999
).
20.
C. J.
Elkins
and
J. K.
Eaton
, “
Turbulent heat and momentum transport on a rotating disk
,”
J. Fluid Mech.
402
,
225
253
(
2000
).
21.
C.
Subramanian
and
R.
Antonia
, “
Effect of Reynolds number on a slightly heated turbulent boundary layer
,”
Int. J. Heat Mass Transfer
24
,
1833
1846
(
1981
).
22.
M.
Gibson
,
C.
Verriopoulos
, and
N.
Vlachos
, “
Turbulent boundary layer on a mildly curved convex surface
,”
Exp. Fluids
2
,
17
24
(
1984
).
23.
J. M.
Wallace
, “
Quadrant analysis in turbulence research: History and evolution
,”
Annu. Rev. Fluid Mech.
48
,
131
158
(
2016
).
24.
M.
Turkyilmazoglu
, “
Flow and heat simultaneously induced by two stretchable rotating disks
,”
Phys. Fluids
28
,
043601
(
2016
).
25.
J. C.
Maxwell
,
A Treatise on Electricity and Magnetism
(
Clarendon Press
,
1881
), Vol. 1.
26.
S. K.
Das
,
S. U.
Choi
, and
H. E.
Patel
, “
Heat transfer in nanofluids—A review
,”
Heat Transfer Eng.
27
,
3
19
(
2006
).
27.
S. U.
Choi
and
J. A.
Eastman
, “
Enhancing thermal conductivity of fluids with nanoparticles
,” Technical Report ANL/MSD/CP-84938; CONF-951135-29,
Argonne National Laboratory
,
IL, USA
,
1995
.
28.
K.
Khanafer
,
K.
Vafai
, and
M.
Lightstone
, “
Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids
,”
Int. J. Heat Mass Transfer
46
,
3639
3653
(
2003
).
29.
Y.
Xuan
and
Q.
Li
, “
Investigation on convective heat transfer and flow features of nanofluids
,”
J. Heat Transfer
125
,
151
155
(
2003
).
30.
S. Z.
Heris
,
M. N.
Esfahany
, and
S. G.
Etemad
, “
Experimental investigation of convective heat transfer of Al2O3/water nanofluid in circular tube
,”
Int. J. Heat Fluid Flow
28
,
203
210
(
2007
).
31.
C. T.
Nguyen
,
G.
Roy
,
C.
Gauthier
, and
N.
Galanis
, “
Heat transfer enhancement using Al2O3–water nanofluid for an electronic liquid cooling system
,”
Appl. Therm. Eng.
27
,
1501
1506
(
2007
).
32.
M.
Alinia
,
D.
Ganji
, and
M.
Gorji-Bandpy
, “
Numerical study of mixed convection in an inclined two sided lid driven cavity filled with nanofluid using two-phase mixture model
,”
Int. Commun. Heat Mass Transfer
38
,
1428
1435
(
2011
).
33.
M.
Goodarzi
,
M.
Safaei
,
K.
Vafai
,
G.
Ahmadi
,
M.
Dahari
,
S.
Kazi
, and
N.
Jomhari
, “
Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model
,”
Int. J. Therm. Sci.
75
,
204
220
(
2014
).
34.
B.
Ghasemi
and
S.
Aminossadati
, “
Brownian motion of nanoparticles in a triangular enclosure with natural convection
,”
Int. J. Therm. Sci.
49
,
931
940
(
2010
).
35.
J.
Koo
and
C.
Kleinstreuer
, “
Laminar nanofluid flow in microheat-sinks
,”
Int. J. Heat Mass Transfer
48
,
2652
2661
(
2005
).
36.
J.
Buongiorno
, “
Convective transport in nanofluids
,”
J. Heat Transfer
128
,
240
250
(
2006
).
37.
A.
Mahajan
and
M. K.
Sharma
, “
Penetrative convection in magnetic nanofluids via internal heating
,”
Phys. Fluids
29
,
034101
(
2017
).
38.
A.
Avramenko
,
I.
Shevchuk
,
S.
Abdallah
,
D.
Blinov
, and
A.
Tyrinov
, “
Self-similar analysis of fluid flow, heat, and mass transfer at orthogonal nanofluid impingement onto a flat surface
,”
Phys. Fluids
29
,
052005
(
2017
).
39.
T.
Hayat
,
T.
Muhammad
,
A.
Alsaedi
, and
B.
Ahmad
, “
Three-dimensional flow of nanofluid with Cattaneo–Christov double diffusion
,”
Results Phys.
6
,
897
903
(
2016
).
40.
M.
Ramzan
,
M.
Bilal
,
J. D.
Chung
,
D. C.
Lu
, and
U.
Farooq
, “
Impact of generalized Fourier’s and Fick’s laws on MHD 3D second grade nanofluid flow with variable thermal conductivity and convective heat and mass conditions
,”
Phys. Fluids
29
,
093102
(
2017
).
41.
N.
Bachok
,
A.
Ishak
, and
I.
Pop
, “
Flow and heat transfer over a rotating porous disk in a nanofluid
,”
Phys. B
406
,
1767
1772
(
2011
).
42.
H. E.
Patel
,
K.
Anoop
,
T.
Sundararajan
, and
S. K.
Das
, “
A micro-convection model for thermal conductivity of nanofluids
,” in
International Heat Transfer Conference
(
Begel House, Inc.
,
2006
), p.
13
.
43.
M.
Turkyilmazoglu
, “
Nanofluid flow and heat transfer due to a rotating disk
,”
Comput. Fluids
94
,
139
146
(
2014
).
44.
M.
Mustafa
,
J. A.
Khan
,
T.
Hayat
, and
A.
Alsaedi
, “
On Bödewadt flow and heat transfer of nanofluids over a stretching stationary disk
,”
J. Mol. Liq.
211
,
119
125
(
2015
).
45.
A.
Mushtaq
and
M.
Mustafa
, “
Computations for nanofluid flow near a stretchable rotating disk with axial magnetic field and convective conditions
,”
Results Phys.
7
,
3137
3144
(
2017
).
46.
É.
Séverac
,
S.
Poncet
,
É.
Serre
, and
M.-P.
Chauve
, “
Large eddy simulation and measurements of turbulent enclosed rotor-stator flows
,”
Phys. Fluids
19
,
085
113
(
2007
).
47.
S.
Makino
,
M.
Inagaki
, and
M.
Nakagawa
, “
Laminar-turbulence transition over the rotor disk in an enclosed rotor-stator cavity
,”
Flow, Turbul. Combust.
95
,
399
413
(
2015
).
48.
V.
Ekman
, “
On the influence of the earth’s rotation on ocean-currents
,”
Ark. Mat., Astron. Fys.
2
,
1
53
(
1905
).
49.
U. T.
Bödewadt
, “
Die drehströmung über festem grunde
,”
ZAMM- Z. Angew. Math. Mech.
20
,
241
253
(
1940
).
50.
J.
Tu
,
G. H.
Yeoh
, and
C.
Liu
,
Computational Fluid Dynamics: A Practical Approach
(
Butterworth-Heinemann
,
2012
).
51.
F.
Moukalled
,
L.
Mangani
,
M.
Darwish
 et al,
The Finite Volume Method in Computational Fluid Dynamics
(
Springer
,
2016
).
52.
R. I.
Issa
,
A.
Gosman
, and
A.
Watkins
, “
The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme
,”
J. Comput. Phys.
62
,
66
82
(
1986
).
53.
F.
Nicoud
and
F.
Ducros
, “
Subgrid-scale stress modelling based on the square of the velocity gradient tensor
,”
Flow, Turbul. Combust.
62
,
183
200
(
1999
).
54.
M.
Antonopoulos-Domis
, “
Large-eddy simulation of a passive scalar in isotropic turbulence
,”
J. Fluid Mech.
104
,
55
79
(
1981
).
55.
D. D.
Gray
and
A.
Giorgini
, “
The validity of the Boussinesq approximation for liquids and gases
,”
Int. J. Heat Mass Transfer
19
,
545
551
(
1976
).
56.
M.
Manninen
,
V.
Taivassalo
,
S.
Kallio
 et al,
On the Mixture Model for Multiphase Flow
(
VTT Publications
,
1996
).
57.
M.
Rebay
,
S.
Kakaç
, and
R. M.
Cotta
,
Microscale and Nanoscale Heat Transfer: Analysis, Design, and Application
(
CRC Press
,
2016
).
58.
G.
McNab
and
A.
Meisen
, “
Thermophoresis in liquids
,”
J. Colloid Interface Sci.
44
,
339
346
(
1973
).
59.
A.
Einstein
, “
Eine neue bestimmung der moleküldimensionen
,”
Ann. Phys.
324
,
289
306
(
1906
).
60.
H.
Brinkman
, “
The viscosity of concentrated suspensions and solutions
,”
J. Chem. Phys.
20
,
571
(
1952
).
61.
N. A. A.
Bakar
,
N.
Bachok
, and
N. M.
Arifin
, “
Nanofluid flow using Buongiorno model over a stretching sheet and thermophysical properties of nanoliquids
,”
Indian J. Sci. Technol.
9
,
1
9
(
2016
).
62.
T.
Bridel-Bertomeu
,
L.
Gicquel
, and
G.
Staffelbach
, “
Large scale motions of multiple limit-cycle high Reynolds number annular and toroidal rotor/stator cavities
,”
Phys. Fluids
29
,
065115
(
2017
).
63.
D.
Fernando
,
S.
Gao
, and
S.
Garrett
, “
The effect of surface roughness on rotor-stator cavity flows
,”
Phys. Fluids
30
,
064103
(
2018
).
64.
J.
Jeong
and
F.
Hussain
, “
On the identification of a vortex
,”
J. Fluid Mech.
285
,
69
94
(
1995
).
65.
C.
Hu
,
P.
Heng
,
M.
Bai
,
J.
Lv
,
Y.
Wang
, and
X.
Li
, “
Numerical study of nanofluids flow characteristics using LES–Lagrange method and molecular dynamics simulation
,” in
ASME 2013 4th International Conference on Micro/Nanoscale Heat and Mass Transfer
(
American Society of Mechanical Engineers
,
2013
), p.
V001T02A001
.
66.
O.
Ghaffari
,
A.
Behzadmehr
, and
H.
Ajam
, “
Turbulent mixed convection of a nanofluid in a horizontal curved tube using a two-phase approach
,”
Int. Commun. Heat Mass Transfer
37
,
1551
1558
(
2010
).
67.
J.
Pellé
and
S.
Harmand
, “
Heat transfer measurements in an opened rotor–stator system air-gap
,”
Exp. Therm. Fluid Sci.
31
,
165
180
(
2007
).
68.
L.
Dorfman
,
Hydrodynamic Resistance and Heat Loss of Rotating Solids
(
Oliver and Boyd
,
Edinburgh and London
,
1963
).
69.
C.
Xu
, “
Nonlinear least squares: Trust region methods nonlinear least squares: Trust region methods
,” in
Encyclopedia of Optimization
, edited by
C. A.
Floudas
and
P. M.
Pardalos
(
Springer US
,
Boston, MA
,
2009
), pp.
2630
2637
.
70.
A. C.
Cameron
and
F. A.
Windmeijer
, “
An R-squared measure of goodness of fit for some common nonlinear regression models
,”
J. Econom.
77
,
329
342
(
1997
).
71.
M.
Jeremy
, “
R squared, adjusted R squared
,” in
Encyclopedia of Statistics in Behavioral Science
(
American Cancer Society
,
2005
).
72.
A.-N.
Spiess
and
N.
Neumeyer
, “
An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: A Monte Carlo approach
,”
BMC Pharmacol.
10
,
6
(
2010
).
You do not currently have access to this content.