Abstract

The influence of trigonometric cosine, square, sawtooth, and triangular wave types of magnetic-field modulation in nanoliquid within Hele-Shaw cell is studied in this paper utilizing linear/nonlinear explorations. The solvability condition to the third-order solution of the referred model equation has been imposed to get the cubic Ginzburg–Landau equation (GBL-equation) which is utilized to measure the rate of heat (or mass) transfer. In the sequel, the influence of the nondimensional parameters is discussed graphically in detail. It is demonstrated that Prandtl number (Pr)/magnetic Prandtl number (Prm)/Lewis-number (Le)/redefined diffusivity-ratio (NA)/concentration Rayleigh-number (RS1) and magnitude of the magnetic-modulation (δ) destabilize the system, that is, the heat/mass transfer increases. On the other hand, nanoliquid magnetic-number (Q), Hele–Shaw number (Hs), and modulating-frequency (ω) stabilize the system. The outcomes demonstrate that the magnetic-field modulation can be imposed significantly to increase or decrease the heat/mass transfer.

References

1.
Choi
,
S.
,
1995
, Enhancing thermal conductivity of fluids with nanoparticles,
Argonne National Lab. (ANL)
,
Argonne, IL
, Technical Report No. ANL/MSD/CP-84938; CONF-951135-29.
2.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Mass Transfer-Trans. ASME
,
128
(
3
), pp.
240
250
.10.1115/1.2150834
3.
Neild
,
D. A.
, and
Bejan
,
A.
,
2017
,
Convection in Porous Media
,
Springer-Verlag
,
New York
.
4.
Hele-Shaw
,
H. S.
,
1898
, “
Experiments on the Nature of Surface Resistance of Water and Streamline Motion Under Certain Experimental Conditions
,”
Trans. Inst. Nav. Archtects
,
40
, pp.
21
46
.https://cir.nii.ac.jp/crid/1570009750005893504
5.
Wooding
,
R. A.
,
1960
, “
Instability of a Viscous Liquid of Variable Density in a Vertical Hele–Shaw Cell
,”
J. Fluid Mech.
,
7
(
4
), pp.
501
515
.10.1017/S0022112060000256
6.
Hartline
,
B. K.
, and
Lister
,
C.
,
1977
, “
Thermal Convection in a Hele-Shaw Cell
,”
J. Fluid Mech.
,
79
(
2
), pp.
379
389
.10.1017/S0022112077000202
7.
Aniss
,
S.
,
Souhar
,
M.
, and
Brancher
,
J. P.
,
1995
, “
Asymptotic Study and Weakly Nonlinear Analysis at the Onset of Rayleigh–Bénard Convection in Hele–Shaw Cell
,”
Phys. Fluids
,
7
(
5
), pp.
926
934
.10.1063/1.868568
8.
Bhadauria
,
B.
,
Bhatia
,
P.
, and
Debnath
,
L.
,
2005
, “
Convection in Hele–Shaw Cell With Parametric Excitation
,”
Int. J. Non-Linear Mech.
,
40
(
4
), pp.
475
484
.10.1016/j.ijnonlinmec.2004.07.010
9.
Wakif
,
A.
,
Boulahia
,
Z.
, and
Sehaqui
,
R.
,
2016
, “
The Effect of the Rotation on the Onset of Convection in a Hele–Shaw Cell Saturated by a Newtonian Nanofluid: A Revised Model
,”
Elixir Therm. Eng.
,
92
, pp.
38976
38985
.https://www.researchgate.net/publication/299063586_The_Effect_of_the_Rotation_on_the_Onset_of_Convection_in_a_Hele-Shaw_Cell_Saturated_by_a_Newtonian_Nanofluid_A_Revised_Model
10.
Boulal
,
T.
,
Aniss
,
S.
,
Belhaq
,
M.
, and
Azouani
,
A.
,
2008
, “
Effect of Quasi-Periodic Gravitational Modulation on the Convective Instability in Hele–Shaw Cell
,”
Int. J. Non-Linear Mech.
,
43
(
9
), pp.
852
857
.10.1016/j.ijnonlinmec.2008.05.004
11.
Souhar
,
K.
, and
Aniss
,
S.
,
2012
, “
Effect of Coriolis Force on the Thermosolutal Convection Threshold in a Rotating Annular Hele–Shaw Cell
,”
Heat Mass Transfer
,
48
(
1
), pp.
175
182
.10.1007/s00231-011-0849-x
12.
Yadav
,
D.
,
2019
, “
The Effect of Pulsating Throughflow on the Onset of Magneto Convection in a Layer of Nanofluid Confined Within a Hele–Shaw Cell
,”
Proc. Inst. Mech. Eng., Part E
,
233
(
5
), pp.
1074
1085
.10.1177/0954408919836362
13.
Bhadauria
,
B. S.
, and
Kumar
,
A.
,
2021
, “
Throughflow and Gravity Modulation Effect on Thermal Instability in a Hele–Shaw Cell Saturated by Nanofluid
,”
J. Porous Media
,
24
(
6
), pp.
31
51
.10.1615/JPorMedia.2021035435
14.
Thompson
,
W.
,
1951
, “
CXLIII. Thermal Convection in a Magnetic Field
,”
London, Edinburgh, Dublin Philos. Mag. J. Sci.
,
42
(
335
), pp.
1417
1432
.10.1080/14786445108560961
15.
Chandrasekhar
,
S.
,
1961
,
Hydrodynamic and Hydromagnetic Stability
,
Oxford University Press
,
London
.
16.
Nakagawa
,
Y.
,
1957
, “
Experiments on the Inhibition of Thermal Convection by a Magnetic Field
,”
Proc. R. Soc. London. Ser. A.
,
240
(
1220
), pp.
108
113
.10.1098/rspa.1957.0154
17.
Nakagawa
,
Y.
,
1959
, “
Experiments on the Instability of a Layer of Mercury Heated From Below and Subject to the Simultaneous Action of a Magnetic Field and Rotation. II
,”
Proc. R. Soc. London. Ser. A.
249
(
1256
), pp.
138
145
.https://www.jstor.org/stable/100571
18.
Finlayson
,
B.
,
1970
, “
Convective Instability of Ferromagnetic Fluids
,”
J. Fluid Mech.
,
40
(
04
), pp.
753
767
.10.1017/S0022112070000423
19.
Gotoh
,
K.
, and
Yamada
,
M.
,
1982
, “
Thermal Convection in a Horizontal Layer of Magnetic Fluids
,”
J. Phys. Soc. Jpn.
,
51
(
9
), pp.
3042
3048
.10.1143/JPSJ.51.3042
20.
Ozoe
,
H.
, and
Maruo
,
E.
,
1987
, “
Magnetic and Gravitational Natural Convection of Melted Silicon–Two-Dimensional Numerical Computations for the Rate of Heat Transfer: Heat Transfer, Combustion, Power, Thermophysical Properties
,”
JSME Int. J.
,
30
(
263
), pp.
774
784
.10.1299/jsme1987.30.774
21.
Siddheshwar
,
P.
, and
Pranesh
,
S.
,
2000
, “
Effect of Temperature/Gravity Modulation on the Onset of Magneto-Convection in Electrically Conducting Fluids With Internal Angular Momentum
,”
J. Magn. Magn. Mater.
,
219
(
2
), pp.
153
162
.10.1016/S0304-8853(00)00438-8
22.
Bhadauria
,
B.
,
2006
, “
Time-Periodic Heating of Rayleigh–Bénard Convection in a Vertical Magnetic Field
,”
Phys. Scr.
,
73
(
3
), pp.
296
302
.10.1088/0031-8949/73/3/010
23.
Bhadauria
,
B.
,
2008
, “
Combined Effect of Temperature Modulation and Magnetic Field on the Onset of Convection in an Electrically Conducting-Fluid-Saturated Porous Medium
,”
ASME J. Heat Mass Transfer-Trans. ASME
,
130
(
5
), p.
052601
.10.1115/1.2885871
24.
Siddheshwar
,
P.
,
Bhadauria
,
B.
,
Mishra
,
P.
, and
Srivastava
,
A. K.
,
2012
, “
Study of Heat Transport by Stationary Magneto-Convection in a Newtonian Liquid Under Temperature or Gravity Modulation Using Ginzburg–Landau Model
,”
Int. J. Non-Linear Mech.
,
47
(
5
), pp.
418
425
.10.1016/j.ijnonlinmec.2011.06.006
25.
Yadav
,
D.
,
Bhargava
,
R.
, and
Agrawal
,
G.
,
2013
, “
Thermal Instability in a Nanofluid Layer With a Vertical Magnetic Field
,”
J. Eng. Math.
,
80
(
1
), pp.
147
164
.10.1007/s10665-012-9598-1
26.
Gupta
,
U.
,
Ahuja
,
J.
, and
Wanchoo
,
R.
,
2013
, “
Magneto Convection in a Nanofluid Layer
,”
Int. J. Heat Mass Transfer
,
64
, pp.
1163
1171
.10.1016/j.ijheatmasstransfer.2013.05.035
27.
Sheikholeslami
,
M.
,
Bani Sheykholeslami
,
F.
,
Khoshhal
,
S.
,
Mola-Abasia
,
H.
,
Ganji
,
D. D.
, and
Rokni
,
H. B.
,
2014
, “
Effect of Magnetic Field on Cu–Water Nanofluid Heat Transfer Using GMDH–Type Neural Network
,”
Neural Comput. Appl.
,
25
(
1
), pp.
171
178
.10.1007/s00521-013-1459-y
28.
Bansal
,
S.
, and
Chatterjee
,
D.
,
2015
, “
Magneto-Convective Transport of Nanofluid in a Vertical Lid-Driven Cavity Including a Heat-Conducting Rotating Circular Cylinder
,”
Numer. Heat Transfer, Part A
,
68
(
4
), pp.
411
431
.10.1080/10407782.2014.986361
29.
Aniss
,
S. D.
,
Belhaq
,
M.
, and
Souhar
,
M.
,
2001
, “
Effects of a Magnetic Modulation on the Stability of a Magnetic Liquid Layer Heated From Above
,”
ASME J. Heat Mass Transfer-Trans. ASME
,
123
(
3
), pp.
428
433
.10.1115/1.1370501
30.
Bhadauria
,
B.
, and
Kiran
,
P.
,
2014
, “
Weak Nonlinear Analysis of Magneto–Convection Under Magnetic Field Modulation
,”
Phys. Scr.
,
89
(
9
), p.
095209
.10.1088/0031-8949/89/9/095209
31.
Keshri
,
O. P.
,
Kumar
,
A.
, and
Gupta
,
V. K.
,
2019
, “
Effect of Internal Heat Source on Magneto-Stationary Convection of Couple Stress Fluid Under Magnetic Field Modulation
,”
Chin. J. Phys.
,
57
, pp.
105
115
.10.1016/j.cjph.2018.12.006
32.
Meghana
,
J.
, and
Pranesh
,
S.
,
2021
, “
Individual Effects of Four Types of Rotation Modulation on Rayleigh–Bénard Convection in a Ferromagnetic Fluid With Couple Stress
,”
Heat Transfer
,
50
(
7
), pp.
6795
6815
.10.1002/htj.22204
33.
Kuznetsov
,
A.
, and
Nield
,
D.
,
2010
, “
Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: Brinkman Model
,”
Transp. Porous Media
,
81
(
3
), pp.
409
422
.10.1007/s11242-009-9413-2
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