A numerical study of the natural convection flow in a porous cavity with wavy bottom and top walls having sinusoidal temperature distributions on vertical walls filled with a nanofluid is numerically investigated. The mathematical model has been formulated in dimensionless stream function and temperature taking into account the Darcy–Boussinesq approximation and the Buongiorno's nanofluid model. The boundary-value problem has been solved numerically on the basis of a second-order accurate finite difference method. Efforts have been focused on the effects of five types of influential factors such as the Rayleigh (Ra = 10–300) and Lewis (Le = 1–1000) numbers, the buoyancy-ratio parameter (Nr = 0.1–0.4), the Brownian motion parameter (Nb = 0.1–0.4), and the thermophoresis parameter (Nt = 0.1–0.4) on the fluid flow and heat transfer characteristics. It has been found that the average Nusselt and Sherwood numbers are increasing functions of the Rayleigh number, buoyancy- ratio parameter, and thermophoresis parameter, and decreasing functions of the Lewis number and Brownian motion parameter.

References

References
1.
Nield
,
D. A.
, and
Bejan
,
A.
,
2013
,
Convection in Porous Media
,
4th ed.
,
Springer
,
New York
10.1007/978-1-4614-5541-7.
2.
Ingham
,
D. B.
, and
Pop
,
I.
, eds.,
2005
,
Transport Phenomena in Porous Media III
,
Elsevier
,
Oxford, UK
.
3.
Vafai
,
K.
, ed.,
2005
,
Handbook of Porous Media
,
Taylor and Francis
,
New York
.
4.
Pop
,
I.
, and
Ingham
,
D. B.
,
2001
,
Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media
,
Pergamon
,
Oxford, UK
.
5.
Bejan
,
A.
,
Dincer
,
I.
,
Lorente
,
S.
,
Miguel
,
A. F.
, and
Reis
,
A. H.
,
2004
,
Porous and Complex Flow Structures in Modern Technologies
,
Springer
,
New York
.
6.
Vadasz
,
P.
, ed.,
2008
,
Emerging Topics in Heat and Mass Transfer in Porous Media
,
Springer
,
New York
.
7.
de Lemos
,
M. J. S.
,
2012
,
Turbulence in Porous Media. Modeling and Applications
,
2nd ed.
,
Elsevier
,
Oxford, UK
.
8.
Aydin
,
O.
,
Unal
,
A.
, and
Ayhan
,
T.
,
1999
, “
Natural Convection in Rectangular Enclosures Heated From One Side and Cooled From the Ceiling
,”
Int. J. Heat Mass Transfer
,
42
(
13
), pp.
2345
2355
.10.1016/S0017-9310(98)00319-6
9.
Sarris
,
I. E.
,
Leakakis
,
I.
, and
Vlachos
,
N. S.
,
2002
, “
Natural Convection in a 2D Enclosure With Sinusoidal Upper Wall Temperature
,”
Numer. Heat Transfer, Part A
,
42
(
5
), pp.
513
530
.10.1080/10407780290059675
10.
Poulikakos
,
D.
,
1985
, “
Natural Convection in a Confined Fluid-Filled Space Driven by a Single Vertical Wall With Warm and Cold Regions
,”
ASME J. Heat Transfer
,
107
(
4
), pp.
867
876
.10.1115/1.3247515
11.
Bilgen
,
E.
,
Wang
,
X.
,
Vasseur
,
P.
,
Meng
,
F.
, and
Rabillard
,
L.
,
1995
, “
On the Periodic Conditions to Simulate Mixed Convection Heat Transfer in Horizontal Channels
,”
Numer. Heat Transfer, Part A
,
27
(
4
), pp.
461
472
.10.1080/10407789508913712
12.
Lage
,
J. L.
, and
Bejan
,
A.
,
1993
, “
The Resonance of Natural Convection in an Enclosure Heated Periodically From the Side
,”
Int. J. Heat Mass Transfer
,
36
(8), pp.
2027
2038
.10.1016/S0017-9310(05)80134-6
13.
Wright
,
S.
, and
Rawson
,
H.
,
1973
, “
Calculation of Natural Convection in a Rectangular Cell Containing Glass With Specified Temperatures on the Boundaries
,”
Glass Technol.
,
14
, pp.
42
49
.
14.
Burley
,
D. M.
,
Moult
,
A.
, and
Rawson
,
H.
,
1978
, “
Application of the Finite Element Method to Calculate Flow Patterns in Glass Tank Furnaces
,”
Glass Technol.
,
19
, pp.
86
91
.
15.
Masuda
,
H.
,
Ebata
,
A.
,
Teramae
,
K.
, and
Hishinuma
,
N.
,
1993
, “
Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra Fine Particles
,”
Netsu Bussei
,
7
(
4
), pp.
227
233
.10.2963/jjtp.7.227
16.
Haddad
,
Z.
,
Oztop
,
H. F.
,
Abu-Nada
,
E.
, and
Mataoui
,
A.
,
2012
, “
A Review on Natural Convective Heat Transfer of Nanofluids
,”
Renewable Sustainable Energy Rev.
,
16
(
7
), pp.
5363
5378
.10.1016/j.rser.2012.04.003
17.
Haddad
,
Z.
,
Abu-Nada
,
E.
,
Oztop
,
H. F.
, and
Mataoui
,
A.
,
2012
, “
Natural Convection in Nanofluids: Are the Thermophoresis and Brownian Motion Effects Significant in Nanofluid Heat Transfer Enhancement
?,”
Int. J. Therm. Sci.
,
57
, pp.
152
162
.10.1016/j.ijthermalsci.2012.01.016
18.
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
(
5
), pp.
1326
1336
.10.1016/j.ijheatfluidflow.2008.04.009
19.
Misirlioglu
,
A.
,
Cihat Baytas
,
A.
, and
Pop
,
I.
,
2005
, “
Free Convection in a Wavy Cavity Filled With a Porous Medium
,”
Int. J. Heat Mass Transfer
,
48
(
9
), pp.
1840
1850
.10.1016/j.ijheatmasstransfer.2004.12.005
20.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
,
128
(
3
), pp.
240
250
.10.1115/1.2150834
21.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2013
, “
The Cheng–Minkowycz Problem for Natural Convective Boundary Layer Flow in a Porous Medium Saturated by a Nanofluid: A Revised Model
,”
Int. J. Heat Mass Transfer
,
65
, pp.
682
685
.10.1016/j.ijheatmasstransfer.2013.06.054
22.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2014
, “
Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: A Revised Model
,”
Int. J. Heat Mass Transfer
,
68
, pp.
211
214
.10.1016/j.ijheatmasstransfer.2013.09.026
23.
Deng
,
Q.-H.
, and
Chang
,
J.-J.
,
2008
, “
Natural Convection in a Rectangular Enclosure With Sinusoidal Temperature Distributions on Both Side Walls
,”
Numer. Heat Transfer, Part A
,
54
(
5
), pp.
507
524
.10.1080/01457630802186080
24.
Oztop
,
H. F.
,
Abu-Nada
,
E.
,
Varol
,
Y.
, and
Chamkha
,
A.
,
2011
, “
Natural Convection in Wavy Enclosures With Volumetric Heat Sources
,”
Int. J. Therm. Sci.
,
50
(
4
), pp.
502
514
.10.1016/j.ijthermalsci.2010.10.015
25.
Walker
,
K. L.
, and
Homsy
,
G. M.
,
1978
, “
Convection in a Porous Cavity
,”
J. Fluid Mech.
,
87
, pp.
338
363
.
26.
Baytas
,
A. C.
, and
Pop
,
I.
,
1999
, “
Free Convection in Oblique Enclosures Filled With a Porous Medium
,”
Int. J. Heat Mass Transfer
,
42
(
6
), pp.
1047
1057
.10.1016/S0017-9310(98)00208-7
27.
Aleshkova
,
I. A.
, and
Sheremet
,
M. A.
,
2010
, “
Unsteady Conjugate Natural Convection in a Square Enclosure Filled With a Porous Medium
,”
Int. J. Heat Mass Transfer
,
53
(
23–24
), pp.
5308
5320
.10.1016/j.ijheatmasstransfer.2010.07.025
28.
Sheremet
,
M. A.
, and
Trifonova
,
T. A.
,
2013
, “
Unsteady Conjugate Natural Convection in a Vertical Cylinder Partially Filled With a Porous Medium
,”
Numer. Heat Transfer, Part A
,
64
(
12
), pp.
994
1015
.10.1080/10407782.2013.811973
29.
Sheremet
,
M. A.
,
Grosan
,
T.
, and
Pop
,
I.
,
2014
, “
Free Convection in Shallow and Slender Porous Cavities Filled by a Nanofluid Using Buongiorno's Model
,”
ASME J. Heat Transfer
,
136
(
8
), p.
082501
.10.1115/1.4027355
30.
Sheremet
,
M. A.
, and
Pop
,
I.
,
2014
, “
Conjugate Natural Convection in a Square Porous Cavity Filled by a Nanofluid Using Buongiorno's Mathematical Model
,”
Int. J. Heat Mass Transfer
,
79
, pp.
137
145
.10.1016/j.ijheatmasstransfer.2014.07.092
31.
Samarski
,
A. A.
,
1983
,
Theory of Difference Schemes
,
Nauka
,
Moscow
.
32.
Kimura
,
S.
, and
Bejan
,
A.
,
1983
, “
The “Heatline” Visualization of Convective Heat Transfer
,”
ASME J. Heat Transfer
,
105
(
4
), pp.
916
919
.10.1115/1.3245684
33.
Celli
,
M.
,
2013
, “
Non-Homogeneous Model for a Side Heated Square Cavity Filled With a Nanofluid
,”
Int. J. Heat Fluid Flow
,
44
, pp.
327
335
.10.1016/j.ijheatfluidflow.2013.07.002
You do not currently have access to this content.