Abstract

The stability of nanofluid flow in a vertical channel packed with a porous medium is examined for the local thermal nonequilibrium state of the fluid, particle, and solid–matrix phases. The effects of Brownian motion along with thermophoresis are incorporated in the nanofluid model. The Darcy–Brinkman model for the flow in a porous medium and three-field model, each representing the fluid, particle, and solid–matrix phases separately, for the temperature is used. A normal mode analysis is used to obtain the eigenvalue problem for the perturbed state, which is then solved using the Chebyshev spectral collocation technique. The critical Rayleigh number and corresponding wavenumber are presented graphically for the effect of different local thermal nonequilibrium parameters. It is noticed that the influence of local thermal nonequilibrium (LTNE) parameters on convective instability is significant.

References

1.
Horton
,
C. W.
, and
Rogers
,
F. T.
, Jr.
,
1945
, “
Convection Currents in a Porous Medium
,”
J. Appl. Phys
,
16
(
6
), pp.
367
370
.10.1063/1.1707601
2.
Lapwood
,
E. R.
,
1948
, “
Convection of a Fluid in a Porous Medium
,”
Math. Proc. Cambridge Philos. Soc.
,
44
(
4
), pp.
508
521
.10.1017/S030500410002452X
3.
Nield
,
D. A.
, and
Bejan
,
A.
,
2013
,
Convection in Porous Media
, 4th ed.,
Springer
,
New York
.
4.
Vafai
,
K.
,
2015
,
Handbook of Porous Media
, 3rd ed.,
CRC Press, Taylor and Francis Group
,
Boca Raton, FL
.
5.
Bera
,
P.
, and
Khandelwal
,
M. K.
,
2016
, “
A Thermal Non-Equilibrium Perspective on Instability Mechanism of Non-Isothermal Poiseuille Flow in a Vertical Porous-Media Channel
,”
Int. J. Therm. Sci.
,
105
, pp.
159
173
.10.1016/j.ijthermalsci.2016.03.002
6.
Choi
,
S. U. S.
, and
Eastman
,
J. A.
,
1995
, “
Enhancing Thermal Conductivity of Fluids With Nanoparticles
,” Argonne National Lab, Lemont, IL, pp.
99
105
, Report No.
ANL/MSD/CP-84938
.https://www.osti.gov/biblio/196525-enhancing-thermal-conductivity-fluids-nanoparticles
7.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer-Trans. ASME
,
128
(
3
), pp.
240
250
.10.1115/1.2150834
8.
Tzou
,
D. Y.
,
2008
, “
Instability of Nanofluids in Natural Convection
,”
ASME J. Heat Transfer-Trans. ASME
,
130
(
7
), p.
072401
.10.1115/1.2908427
9.
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.2007.09.014
10.
Kuznetsov
,
A. V.
, and
Nield
,
D. A.
,
2010
, “
Effect of Local Thermal Non-Equilibrium on the Onset of Convection in a Porous Medium Layer Saturated by a Nanofluid
,”
Transp. Porous Media
,
83
(
2
), pp.
425
436
.10.1007/s11242-009-9452-8
11.
Nield
,
D. A.
, and
Kuznetsov
,
A. V.
,
2010
, “
The Effect of Local Thermal Nonequilibrium on the Onset of Convection in a Nanofluid
,”
ASME J. Heat Transfer-Trans. ASME
,
132
(
5
), p.
052405
.10.1115/1.4000474
12.
Bhadauria
,
B. S.
, and
Agarwal
,
S.
,
2011
, “
Convective Transport in a Nanofluid Saturated Porous Layer With Thermal Non Equilibrium Model
,”
Transp. Porous Media
,
88
(
1
), pp.
107
131
.10.1007/s11242-011-9727-8
13.
Agarwal
,
S.
, and
Bhadauria
,
B. S.
,
2011
, “
Natural Convection in a Nanofluid Saturated Rotating Porous Layer With the Thermal Non-Equilibrium Model
,”
Transp. Porous Media
,
90
(
2
), pp.
627
654
.10.1007/s11242-011-9807-9
14.
Mahajan
,
A.
, and
Sharma
,
M. K.
,
2020
, “
Effects of Local Thermal Nonequilibrium on the Onset of Convection in a Magnetic Nanofluid Layer
,”
Heat Transfer Res
,.,
51
(
7
), pp.
689
705
.10.1615/HeatTransRes.2020031119
15.
Srinivasacharya
,
D.
, and
Barman
,
D.
,
2021
, “
Linear Stability of Convection in a Vertical Channel Filled With Nanofluid Saturated Porous Medium
,”
Heat Transfer
,
50
(
4
), pp.
3220
3239
.10.1002/htj.22025
16.
Vadasz
,
P.
,
2006
, “
Heat Conduction in Nanofluid Suspensions
,”
ASME J. Heat Transfer-Trans. ASME
,
128
(
5
), pp.
465
477
.10.1115/1.2175149
17.
Drazin
,
P. G.
, and
Reid
,
W. H.
,
2004
,
Hydrodynamic Stability
, 2nd ed.,
Cambridge University Press
,
Cambridge
.
18.
Caruto
,
C.
,
Hussaini
,
M. Y.
,
Quarteroni
,
A. M.
, and
Zang
,
T. A.
,
1988
,
Spectral Methods in Fluid Dynamics
, 1st ed.,
Springer-Verlag
,
New York
.
19.
Orszag
,
S. A.
,
1971
, “
Accurate Solution of the Orr–Sommerfeld Stability Equation
,”
J. Fluid Mech
,
50
(
4
), pp.
689
703
.10.1017/S0022112071002842
20.
Squire
,
H. B.
,
1933
, “
On the Stability for Three-Dimensional Disturbances of Viscous Fluid Flow Between Parallel Walls
,”
Proc. R. Soc. London, Ser. A
,
142
(
847
), pp.
621
628
.10.1098/rspa.1933.0193
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