The contribution of the current study is to investigate the mixed convection in an inclined nanofluid filled cavity saturated with a partially layered non-Darcy porous medium. Moreover, due to the advantage of the particle-based methods, we presented the improved version of an incompressible smoothed particle hydrodynamics (ISPH) method. The current ISPH method was improved in boundary conditions treatment using renormalization kernel function. In the current investigation, we assumed that the inclined cavity is filled with a Cu-water nanofluid. The upper half of the cavity is saturated with a non-Darcy porous medium. Here, one domain approach is used for coupling the nanofluid and the porous medium layer. The cooled top wall of the cavity is carrying a tangential unit velocity and the bottom wall is heated. The other two wall sides are adiabatic at zero velocity. Here, we investigated the effects of the Richardson parameter Ri0.0001100, Darcy parameter Da 105102, an inclination angle α090deg and a various solid volume fraction ϕ00.05 on the heat transfer of a Cu-water nanofluid. The obtained results showed that the average Nusselt number decreases as the Richardson number increases. An addition of 1–5% Cu nanoparticles slightly increased the overall heat transfer rate.

References

References
1.
Cummins
,
S. J.
, and
Rudman
,
M.
,
1999
, “
An SPH Projection Method
,”
J. Comput. Phys.
,
152
(
2
), pp.
584
607
.
2.
Yildiz
,
M.
,
Rook
,
R. A.
, and
Suleman
,
A.
,
2009
, “
SPH With the Multiple Boundary Tangent Method
,”
Int. J. Numer. Methods Eng.
,
77
(
10
), pp.
1416
1438
.
3.
Shadloo
,
M. S.
,
Zainali
,
A.
,
Sadek
,
S. H.
, and
Yildiz
,
M.
,
2011
, “
Improved Incompressible Smoothed Particle Hydrodynamics Method for Simulating Flow Around Bluff Bodies
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
9–12
), pp.
1008
1020
.
4.
Shadloo
,
M. S.
,
Zainali
,
A.
,
Yildiz
,
M.
, and
Suleman
,
A.
,
2012
, “
A Robust Weakly Compressible SPH Method and Its Comparison With an Incompressible SPH
,”
Int. J. Numer. Methods Eng.
,
89
(
8
), pp.
939
956
.
5.
Zainali
,
A.
,
Tofighi
,
N.
,
Shadloo
,
M. S.
, and
Yildiz
,
M.
,
2013
, “
Numerical Investigation of Newtonian and Non-Newtonian Multiphase Flows Using ISPH Method
,”
Comput. Methods Appl. Mech. Eng.
,
254
, pp.
99
113
.
6.
Rahmat
,
A.
, and
Yildiz
,
M.
,
2018
, “
A Multiphase ISPH Method for Simulation of Droplet Coalescence and Electro-Coalescence
,”
Int. J. Multiphase Flow
,
105
, pp.
32
44
.
7.
Khayyer
,
A.
,
Gotoh
,
H.
, and
Shao
,
S.
,
2008
, “
Corrected Incompressible SPH Method for Accurate Water-Surface Tracking in Breaking Waves
,”
Coastal Eng.
,
55
(
3
), pp.
236
250
.
8.
Khayyer
,
A.
,
Gotoh
,
H.
, and
Shao
,
S.
,
2009
, “
Enhanced Predictions of Wave Impact Pressure by Improved Incompressible SPH Methods
,”
Appl. Ocean Res.
,
31
(
2
), pp.
111
131
.
9.
Asai
,
M.
,
Aly
,
A. M.
,
Sonoda
,
Y.
, and
Sakai
,
Y.
,
2012
, “
A Stabilized Incompressible SPH Method by Relaxing the Density Invariance Condition
,”
J. Appl. Math.
,
2012
, p.
139583
.
10.
Aly
,
A. M.
,
Asai
,
M.
, and
Sonoda
,
Y.
,
2011
, “
Simulation of Free Falling Rigid Body Into Water by a Stabilized Incompressible SPH Method
,”
Ocean Syst. Eng.
,
1
(
3
), pp.
207
222
.
11.
Aly
,
A. M.
,
Asai
,
M.
, and
Sonda
,
Y.
,
2013
, “
Modelling of Surface Tension Force for Free Surface Flows in ISPH Method
,”
Int. J. Numer. Methods Heat Fluid Flow
,
23
(
3
), pp.
479
498
.
12.
Aly
,
A. M.
, and
Ahmed
,
S. E.
,
2014
, “
An Incompressible Smoothed Particle Hydrodynamics Method for Natural/mixed Convection in a Non-Darcy Anisotropic Porous Medium
,”
Int. J. Heat Mass Transfer
,
77
, pp.
1155
1168
.
13.
Aly
,
A. M.
,
2015
, “
Modeling of Multi-Phase Flows and Natural Convection in a Square Cavity Using an Incompressible Smoothed Particle Hydrodynamics
,”
Int. J. Numer. Methods Heat Fluid Flow
,
25
(
3
), pp.
513
533
.
14.
Aly
,
A. M.
,
2016
, “
Double-Diffusive Natural Convection in an Enclosure Including/Excluding Sloshing Rod Using a Stabilized ISPH Method
,”
Int. Commun. Heat Mass Transfer
,
73
, pp.
84
99
.
15.
Aly
,
A. M.
, and
Raizah
,
Z. A.
,
2016
, “
Double-Diffusive Natural Convection in an Enclosure Filled With Nanofluid Using ISPH Method
,”
Alexandria Eng. J.
,
55
(
4
), pp.
3037
3052
.
16.
Aly
,
A. M.
,
Asai
,
M.
, and
Chamkha
,
A. J.
,
2015
, “
Analysis of Unsteady Mixed Convection in Lid-Driven Cavity Included Circular Cylinders Motion Using an Incompressible Smoothed Particle Hydrodynamics Method
,”
Int. J. Numer. Methods Heat Fluid Flow
,
25
(
8
), pp.
2000
2021
.
17.
Aly
,
A. M.
,
Chamkha
,
A. J.
,
Lee
,
S.-W.
, and
Al-Mudhaf
,
A. F.
,
2016
, “
On Mixed Convection in an Inclined Lid-Driven Cavity With Sinusoidal Heated Walls Using the ISPH Method
,”
Comput. Therm. Sci.: An Int. J.
,
8
(
4
), pp.
337
354
.
18.
Ramadhyani
,
S.
, and
Viskanta
,
R.
,
1987
, “
Natural Convection Flow and Heat Transfer Between a Fluid Layer and a Porous Layer Inside a Rectangular Enclosure
,”
ASME J. Heat Transfer
,
109
(
2
), pp.
363
370
.http://user.engineering.uiowa.edu/~becker/documents.dir/jhr1987.pdf
19.
Beckermann
,
C.
, and
Viskanta
,
R.
, 1988, “
Natural Convection Solid/Liquid Phase Change in Porous Media
,”
Int. J. Heat Mass Transfer
,
31
(1), pp. 35–46.
20.
Singh
,
A.
,
Paul
,
T.
, and
Thorpe
,
G.
,
1999
, “
Natural Convection Due to Heat and Mass Transfer in a Composite System
,”
Heat Mass Transfer
,
35
(
1
), pp.
39
48
.
21.
Hamimid
,
S.
,
Guellal
,
M.
,
Amroune
,
A.
, and
Zeraibi
,
N.
,
2012
, “
Effect of a Porous Layer on the Flow Structure and Heat Transfer in a Square Cavity
,”
Fluid Dyn. Mater. Process.
,
8
(
1
), pp.
69
90
.http://www.techscience.com/doi/10.3970/fdmp.2011.008.069.pdf
22.
Chandran
,
P.
,
Sacheti
,
N. C.
, and
Singh
,
A. K.
,
2013
, “
A Numerical Investigation of a Buoyancy Driven Flow in a Semi-Porous Cavity: Comparative Effects of Ramped and Isothermal Wall Conditions
,”
J. Hydrol. Hydromech.
,
61
(
2
), pp.
103
111
.
23.
Al-Zamily
,
A. M. J.
,
2017
, “
Analysis of Natural Convection and Entropy Generation in a Cavity Filled With Multi-Layers of Porous Medium and Nanofluid With a Heat Generation
,”
Int. J. Heat Mass Transfer
,
106
, pp.
1218
1231
.
24.
Astanina
,
M. S.
,
Sheremet
,
M. A.
,
Oztop
,
H. F.
, and
Abu-Hamdeh
,
N.
,
2018
, “
Mixed Convection of Al2O3-Water Nanofluid in a Lid-Driven Cavity Having Two Porous Layers
,”
Int. J. Heat Mass Transfer
,
118
(
Suppl. C
), pp.
527
537
.
25.
Sheikholeslami
,
M.
, and
Rokni
,
H. B.
,
2018
, “
Magnetic Nanofluid Flow and Convective Heat Transfer in a Porous Cavity Considering Brownian Motion Effects
,”
Phys. Fluids
,
30
(
1
), p.
012003
.
26.
Sheikholeslami
,
M.
, and
Shamlooei
,
M.
,
2017
, “
Convective Flow of Nanofluid Inside a Lid Driven Porous Cavity Using CVFEM
,”
Phys. B: Condens. Matter
,
521
, pp.
239
250
.
27.
Sheikholeslami
,
M.
,
Li
,
Z.
, and
Shamlooei
,
M.
,
2018
, “
Nanofluid MHD Natural Convection Through a Porous Complex Shaped Cavity Considering Thermal Radiation
,”
Phys. Lett. A
,
382
(
24
), pp.
1615
1632
.
28.
Yaghoubi Emami
,
R.
,
Siavashi
,
M.
, and
Shahriari Moghaddam
,
G.
,
2018
, “
The Effect of Inclination Angle and Hot Wall Configuration on Cu-Water Nanofluid Natural Convection Inside a Porous Square Cavity
,”
Adv. Powder Technol.
,
29
(
3
), pp.
519
536
.
29.
Raizah
,
Z. A. S.
,
Aly
,
A. M.
, and
Ahmed
,
S. E.
,
2018
, “
Natural Convection Flow of a Power-Law Non-Newtonian Nanofluid in Inclined Open Shallow Cavities Filled With Porous Media
,”
Int. J. Mech. Sci.
,
140
, pp.
376
393
.
30.
Bilgen
,
E.
, and
Oztop
,
H.
,
2005
, “
Natural Convection Heat Transfer in Partially Open Inclined Square Cavities
,”
Int. J. Heat Mass Transfer
,
48
(
8
), pp.
1470
1479
.
31.
Li
,
H.
, and
Tong
,
S.
,
2016
, “
Natural Convective Heat Transfer in the Inclined Rectangular Cavities With Low Width-to-Height Ratios
,”
Int. J. Heat Mass Transfer
,
93
, pp.
398
407
.
32.
Zhang
,
T.
, and
Che
,
D.
,
2016
, “
Double MRT Thermal Lattice Boltzmann Simulation for MHD Natural Convection of Nanofluids in an Inclined Cavity With Four Square Heat Sources
,”
Int. J. Heat Mass Transfer
,
94
, pp.
87
100
.
33.
Kefayati
,
G. H. R.
,
2018
, “
Double-Diffusive Natural Convection and Entropy Generation of Bingham Fluid in an Inclined Cavity
,”
Int. J. Heat Mass Transfer
,
116
(
Suppl. C
), pp.
762
812
.
34.
Sheremet
,
M. A.
,
Pop
,
I.
, and
Mahian
,
O.
,
2018
, “
Natural Convection in an Inclined Cavity With Time-Periodic Temperature Boundary Conditions Using Nanofluids: Application in Solar Collectors
,”
Int. J. Heat Mass Transfer
,
116
(
Suppl. C
), pp.
751
761
.
35.
Nguyen
,
M. T.
,
Aly
,
A. M.
, and
Lee
,
S.-W.
,
2017
, “
Effect of a Wavy Interface on the Natural Convection of a Nanofluid in a Cavity With a Partially Layered Porous Medium Using the ISPH Method
,”
Numer. Heat Transfer, Part A
,
72
(
1
), pp.
68
88
.
36.
Iwatsu
,
R.
,
Hyun
,
J. M.
, and
Kuwahara
,
K.
,
1993
, “
Mixed Convection in a Driven Cavity With a Stable Vertical Temperature Gradient
,”
Int. J. Heat Mass Transfer
,
36
(
6
), pp.
1601
1608
.
37.
Khanafer
,
K. M.
, and
Chamkha
,
A. J.
,
1999
, “
Mixed Convection Flow in a Lid-Driven Enclosure Filled With a Fluid-Saturated Porous Medium
,”
Int. J. Heat Mass Transfer
,
42
(13), pp.
2465
2481
.
38.
Nithiarasu
,
P.
,
Seetharamu
,
K. N.
, and
Sundararajan
,
T.
,
1997
, “
Natural Convective Heat Transfer in a Fluid Saturated Variable Porosity Medium
,”
Int. J. Heat Mass Transfer
,
40
(
16
), pp.
3955
3967
.
39.
Maxwell
,
J.
,
1904
,
A Treatise on Electricity and Magnetism
,
2nd ed.
,
Oxford University Press
,
Cambridge, UK
.
40.
Brinkman
,
H. C.
,
1952
, “
The Viscosity of Concentrated Suspensions and Solutions
,”
J. Chem. Phys.
,
20
(
4
), p. 571.
41.
Chorin
,
A. J.
,
1968
, “
Numerical Solution of the Navier-Stokes Equations
,”
Math. Comput.
,
22
(
104
), pp.
745
762
.
42.
Ghia
,
U.
,
Ghia
,
K. N.
, and
Shin
,
C. T.
,
1982
, “
High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method
,”
J. Comput. Phys.
,
48
(
3
), pp.
387
411
.
43.
Nguyen
,
T. M.
,
Aly
,
A. M.
, and
Lee
,
S.-W.
,
2018
, “
Improved Wall Boundary Conditions in the Incompressible Smoothed Particle Hydrodynamics Method
,”
Int. J. Numer. Methods Heat Fluid Flow
,
28
(3), pp. 704–725.https://www.emeraldinsight.com/doi/abs/10.1108/HFF-02-2017-0056
44.
Ghazvini
,
M.
, and
Shokouhmand
,
H.
,
2009
, “
Investigation of a Nanofluid-Cooled Microchannel Heat Sink Using Fin and Porous Media Approaches
,”
Energy Convers. Manage.
,
50
(
9
), pp.
2373
2380
.
45.
Muthtamilselvan
,
M.
,
Kandaswamy
,
P.
, and
Lee
,
J.
,
2010
, “
Heat Transfer Enhancement of Copper-Water Nanofluids in a Lid-Driven Enclosure
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
6
), pp.
1501
1510
.
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