Abstract
This paper aimed to study the flow of a nanofluid in a long vertical porous channel when an external uniform magnetic field is impressed. The Buongiorno two-phase model of nanofluid is supposed to be slightly compressible in order to assume the Oberbeck–Boussinesq approximation. The velocity, the induced magnetic field, the temperature, and the nanoparticle volume fraction are analytically obtained. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of plots illustrating the influence of various parameters involved in the problem is presented and discussed.
Issue Section:
Micro/Nanoscale Heat Transfer
References
1.
Choi
,
S. U. S.
, 1995
, “
Enhancing Thermal Conductivity of Fluids with Nanoparticles
,” ASME Fluids Eng. Div
,
231
, pp. 99
–105
.2.
Das
,
S. K.
,
Choi
,
S. U. S.
,
Yu
,
W.
, and
Pradeep
,
Y.
, 2008
, Nanofluids: Science and Technology
,
Wiley
, Hoboken, NJ
.3.
Nield
,
D. A.
, and
Bejan
,
A.
, 2013
, Convection in Porous Media
, 4th ed.,
Springer
,
New York
.4.
Shenoy
,
A.
,
Sheremet
,
M.
, and
Pop
,
I.
, 2016
, Convective Flow and Heat Transfer From Wavy Surfaces: Viscous Fluids, Porous Media and Nanofluids
,
CRC Press/Taylor & Francis Group
,
New York
.5.
Buongiorno
,
J.
, 2006
, “
Convective Transport in Nanofluids
,” ASME J. Heat Transfer
,
128
(3
), pp. 240
–250
.10.1115/1.21508346.
Yacob
,
N. A.
,
Ishak
,
A.
,
Pop
,
I.
, and
Vajravelu
,
K.
, 2011
, “
Boundary Layer Flow Past a Stretching/Shrinking Surface Beneath an External Uniform Shear Flow With a Convective Surface Boundary Condition in a Nanofluid
,” Nanoscale Res. Lett.
,
6
(1
), pp. 1
–7
.10.1186/1556-276X-6-3147.
Sheremet
,
M. A.
,
Pop
,
I.
, and
Rahman
,
M. M.
, 2015
, “
Three-Dimensional Natural Convection in a Porous Enclosure Filled With a Nanofluid Using Buongiorno Mathematical Model
,” Int. J. Heat Mass Transfer
,
82
, pp. 396
–405
.10.1016/j.ijheatmasstransfer.2014.11.0668.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
, 2010
, “
The Onset of Convection in a Horizontal Nanofluid Layer of Finite Depth
,” Eur. J. Mech. B
,
29
(3
), pp. 217
–223
.10.1016/j.euromechflu.2010.02.0039.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
, 2009
, “
Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid
,” Int. J. Heat Mass Transfer
,
52
(25–26
), pp. 5796
–5801
.10.1016/j.ijheatmasstransfer.2009.07.02310.
Azizian
,
R.
,
Doroodchi
,
E.
,
McKrell
,
T.
,
Buongiorno
,
J.
,
Hu
,
L. W.
, and
Moghtaderi
,
B.
, 2014
, “
Effect of Magnetic Field on Laminar Convective Heat Transfer of Magnetite Nanofluids
,” Int. J. Heat Mass Transfer
,
68
, pp. 94
–109
.10.1016/j.ijheatmasstransfer.2013.09.01111.
Borrelli
,
A.
,
Giantesio
,
G.
,
Patria
,
M. C.
,
Rosca
,
N. C.
,
Rosca
,
A. V.
, and
Pop
,
I.
, 2018
, “
Influence of Temperature and Magnetic Field on the Oblique Stagnation-Point Flow for a Nanofluid Past a Vertical Stretching/Shrinking Sheet
,” Int. J. Numer. Methods Heat Fluid Flow
,
28
, pp. 2874
–2894
.10.1108/HFF-12-2017-049712.
Das
,
S.
,
Jana
,
R. N.
, and
Makinde
,
O. D.
, 2015
, “
Mixed Convective Magnetohydrodynamic Flow in a Vertical Channel Filled With Nanofluids
,” Eng. Sci. Tech., Int. J.
,
18
(2
), pp. 244
–255
.10.1016/j.jestch.2014.12.00913.
Hayat
,
T.
,
Rashid
,
M.
,
Imtiaz
,
M.
, and
Alsaedi
,
A.
, 2015
, “
Magnetohydrodynamic (MHD) Flow of Cu-Water Nanofluid Due to a Rotating Disk With Partial Slip
,” AIP Adv.
,
5
(6
), p. 067169
.10.1063/1.492338014.
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
.10.1063/1.501251715.
Tiwari
,
R. J.
, 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
(9–10
), pp. 2002
–2018
.10.1016/j.ijheatmasstransfer.2006.09.03416.
Bird
,
R. B.
,
Stewart
,
W. E.
, and
Lightfoot
,
E. N.
, 2007
, Transport Phenomena
, Revised 2nd ed.,
Wiley & Sons
, Hoboken, NJ
.17.
Tzou
,
D. Y.
, 2008
, “
Thermal Instability of Nanofluids in Natural Convection
,” Int. J. Heat Mass Transfer
,
51
(11–12
), pp. 2967
–2979
.10.1016/j.ijheatmasstransfer.2007.09.01418.
Chandrasekhar
,
S.
, 1981
, Hydrodynamic and Hydromagnetic Stability
,
Dover Publications
,
New York
.19.
Rajagopal
,
K. R.
, 2007
, “
On a Hierarchy of Approximate Models for Flows of Incompressible Fluids Through Porous Solids
,” Math. Models Methods Appl. Sci.
,
17
, pp. 215
–252
.10.1142/S021820250700189920.
Al-Amri Fahad
,
G.
, 2019
, “
Analytical Solution for Fully Developed Flows of Nanofluids in Mixed-Convection Zone Within Vertical Channel
,” Arabian J. Sci. Eng.
,
44
(2
), pp. 739
–752
.10.1007/s13369-018-3260-921.
Aung
,
W.
, and
Worku
,
G.
, 1986
, “
Developing Flow and Flow Reversal in a Vertical Channel With Asymmetric Wall Temperature
,” ASME J. Heat Transfer
,
108
(2
), pp. 299
–304
.10.1115/1.324691922.
Chamkha
,
A. J.
, 2002
, “
On Laminar Hydromagnetic Mixed Convection Flow in a Vertical Channel With Symmetric and Asymmetric Wall Heating Conditions
,” Int. J. Heat Mass Transfer
,
45
(12
), pp. 2509
–2525
.10.1016/S0017-9310(01)00342-823.
Borrelli
,
A.
,
Giantesio
,
G.
, and
Patria
,
M. C.
, 2015
, “
Magnetoconvection of a Micropolar Fluid in a Vertical Channel
,” Int. J. Heat Mass Transfer
,
80
, pp. 614
–625
.10.1016/j.ijheatmasstransfer.2014.09.03124.
Borrelli
,
A.
,
Giantesio
,
G.
, and
Patria
,
M. C.
, 2017
, “
Reverse Flow in Magnetoconvection of Two Immiscible Fluids in a Vertical Channel
,” ASME J. Fluid Eng.
,
139
(10
), p. 101203
.10.1115/1.403667025.
Borrelli
,
A.
,
Giantesio
,
G.
, and
Patria
,
M. C.
, 2013
, “
Numerical Simulations of Three-Dimensional MHD Stagnation-Point Flow of a Micropolar Fluid
,” Comput. Math. Appl.
,
66
, pp. 472
–489
.10.1016/j.camwa.2013.05.02326.
Borrelli
,
A.
,
Giantesio
,
G.
, and
Patria
,
M. C.
, 2013
, “
On the Numerical Solutions of Three-Dimensional MHD Stagnation-Point Flow of a Newtonian Fluid
,” Int. J. Pure Appl. Math.
,
86
(2
), pp. 425
–442
.10.12732/ijpam.v86i2.1627.
Chamkha
,
A. J.
, 2000
, “
Flow of Two-Immiscible Fluids in Porous and Nonporous Channels
,” ASME J. Fluids Eng.
,
122
(1
), pp. 117
–124
.10.1115/1.48323328.
Umavathi
,
J. C.
, and
Sultana
,
J.
, 2011
, “
Mixed Convection of Micropolar Fluid in a Vertical Double-Passage Channel
,” Int. J. Eng. Sci. Tech.
,
3
(4
), pp. 197
–209
.10.4314/ijest.v3i4.68554Copyright © 2020 by ASME
You do not currently have access to this content.
