The steady fully developed mixed convection flow between two vertical parallel plates with asymmetrical thermal and nanoparticle concentration conditions at the walls filled by a nanofluid is studied. The nanofluid model used in this paper takes into account the Brownian diffusion and the thermophoresis effects, and the analysis is based on analytical solutions. Thus, analytical expressions for the fully developed velocity, temperature, and nanoparticle concentration profiles as well as for the Nusselt and Sherwood numbers at the left wall of the channel are given. A numerical solution has been also obtained and compared with the analytical solution, the agreement being very good.

References

1.
Tao
,
L. N.
, 1960, “
On Combined Free and Forced Convection in Channels
,”
ASME Trans. J. Heat Transfer
,
82
, pp.
233
238
.
2.
Beckett
,
P. M.
, 1980, “
Combined Natural- and Forced-Convection Between Parallel Vertical Walls
,”
SIAM J. Appl. Math.
,
39
, pp.
372
384
.
3.
Aung
,
W.
, and
Worku
,
G.
, 1986, “
Theory of Fully Developed, Combined Convection Including Flow Reversal
,”
ASME Trans. J. Heat Transfer
,
108
, pp.
485
488
.
4.
Lavine
,
A. S.
, 1988, “
Analysis of Fully Developed Opposing Mixed Convection Between Inclined Parallel Plates
,”
Heat Mass Transfer
,
23
, pp.
249
257
.
5.
Cheng
,
C. H.
,
Kou
,
H. S.
, and
Huang
,
W. H.
, 1990, “
Flow Reversal and Heat Transfer of Fully Developed Mixed Convection in Vertical Channels
,”
J. Thermophys. Heat Transfer
,
4
, pp.
375
383
.
6.
Hamadah
,
T. T.
, and
Wirtz
,
R. A.
, 1991, “
Analysis of Laminar Fully Developed Mixed Convection in a Vertical Channel with Opposing Buoyancy
,”
ASME Trans. J. Heat Transfer
,
113
, pp.
507
510
.
7.
Chen
,
Y. C.
, and
Chung
,
J. N.
, 1996, “
The Linear Stability of Mixed Convection in a Vertical Channel Flow
,”
J. Fluid Mech.
,
325
, pp.
29
51
.
8.
Barletta
,
A.
, 1999, “
Analysis of Combined Forced and Free Flow in a Vertical Channel with Viscous Dissipation and Isothermal-Isoflux Boundary Conditions
,”
ASME Trans. J. Heat Transfer
,
121
, pp.
349
356
.
9.
Barletta
,
A.
,
Magyari
,
E.
, and
Keller
,
B.
, 2005, “
Dual Mixed Convection Flows in a Vertical Channel
,”
Int. J. Heat Mass Transfer
,
48
, pp.
4835
4845
.
10.
Barletta
,
A.
,
Celli
,
M.
,
Magyari
,
E.
, and
Zanchini
,
E.
, 2007, “
Buoyant MHD Flows in a Vertical Channel: The Levitation Regime
,”
Heat Mass Transfer
,
44
, pp.
1005
1013
.
11.
Boulama
,
K.
, and
Galanis
,
N.
, 2004, “
Analytical Solution for Fully Developed Mixed Convection Between Parallel Vertical Plates with Heat and Mass Transfer
,”
ASME Trans. J. Heat Transfer
,
126
, pp.
381
388
.
12.
Oztop
,
H. F.
, and
Abu-Nada
,
E.
, 2008, “
Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids
,”
Int. J. Heat Fluid Flow
,
29
, pp.
1326
1336
.
13.
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
, MD-Vol. 231 and FED-Vol. 66, pp.
99
105
.
14.
Wong
,
K. V.
, and
De Leon
,
O.
, 2010, “
Applications of Nanofluids: Current and Future
,”
Adv. Mech. Eng.
,
2010
,
519659
.
15.
Buongiorno
,
J.
, 2006, “
Convective Transport in Nanofluids
,”
ASME Trans. J. Heat Transfer
,
128
, pp.
240
250
.
16.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
, 2009, “
The Cheng-Minkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid
,”
Int. J. Heat Mass Transfer
,
52
, pp.
5792
5795
.
17.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
, 2010, “
Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate
,”
Int. J. Therm. Sci.
,
49
, pp.
243
247
.
18.
Khan
,
W. A.
, and
Pop
,
I.
, 2010, “
Boundary-Layer Flow of a Nanofluid Past a Stretching Sheet
,”
Int. J. Heat Mass Transfer
,
53
, pp.
2477
2483
.
19.
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
, pp.
181
191
.
20.
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
, pp.
3639
3653
.
21.
Tiwari
,
R. K.
, and
Das
,
M. K.
, 2007, “
Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids
,”
Int. J. Heat Mass Transfer
,
50
, pp.
2002
2018
.
22.
Aminossadati
,
S. M.
, and
Ghasemi
,
B.
, 2009, “
Natural Convection Cooling of a Localised Heat Source at the Bottom of a Nanofluid-Filled Enclosure
,”
Eur. J. Mech. B/Fluids
,
28
, pp.
630
640
.
23.
Das
,
S. K.
,
Choi
,
S. U.
,
Yu
,
W.
, and
Pradeep
,
T.
, 2007,
Nanofluids: Science and Technology
Wiley
,
Hoboken, NJ
.
24.
Daungthongsuk
,
W.
, and
Wongwises
,
S.
, 2007, “
A Critical Review of Convective Heat Transfer Nanofluids
,”
Renewable Sustainable Energy Rev.
,
11
, pp.
797
817
.
25.
Wang
,
X. Q.
, and
Mujumdar
,
A. S.
, 2008, “
A Review on Nanofluids. Part I: Theoretical and Numerical Investigations
,”
Braz. J. Chem. Eng.
,
25
, pp.
613
630
.
26.
Kakaç
,
S.
, and
Pramuanjaroenkij
,
A.
, 2009, “
Review of Convective Heat Transfer Enhancement with Nanofluids
,”
Int. J. Heat Mass Transfer
,
52
, pp.
3187
3196
.
27.
Barleta
,
A.
, and
Zanchini
,
E.
, 1999, “
On the Choice of the Reference Temperature for Fully-Developed Mixed Convection in a Vertical Channel
,”
Int. J. Heat Mass Transfer
,
42
, pp.
3169
3181
.
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