Unsteady natural convection flow and heat transfer utilizing magnetic nanoparticles in the presence of a sloping magnetic field inside a square enclosure are simulated numerically following nonhomogeneous dynamic model. Four different thermal boundary conditions: constant, parabolic in space, sinusoidally in space, and time for the bottom hot wall are considered. The top wall of the enclosure is cold while the vertical walls are thermally insulated. Galerkin weighted residual finite element method is used to solve the governing nondimensional partial differential equations. For simulations, 12 types of nanofluids consisting magnetite (Fe3O4), cobalt ferrite (CoFe2O4), Mn–Zn ferrite (Mn–ZnFe2O4), and silicon dioxide (SiO2) nanoparticles along with water, engine oil, and kerosene as base fluids are used. The effects of the important model parameters such as Hartmann number, magnetic field sloping angle, and thermal Rayleigh number on the flow fields are investigated. The results show that the average Nusselt number, shear rate, as well as the nanofluid velocity decreases as the Hartmann number intensifies. Moreover, the rate of heat transfer in nanofluid exaggerates with the increase of the thermal Rayleigh number and the magnetic field sloping angle. Sinusoidally varied in space thermal boundary condition at the bottom wall provides the highest average Nusselt number and the shear rate compared to the other types of thermal boundary conditions studied here. For this case, the highest average Nusselt number is obtained for the Mn–ZnFe2O4–Ke nanofluid. On the other hand, Fe3O4–H2O nanofluid delivers the highest shear rate compared to the other premeditated nanofluids.

References

References
1.
Choi
,
S. U. S.
,
1995
, “
Enhancing Thermal Conductivity of Fluids With Nanoparticles
,”
Developments and Applications of Non-Newtonian Flows
, FED-Vol. 231/MD-Vol. 66,
D. A.
Siginer
and
H. P.
Wang
, eds.,
ASME
,
New York
, pp.
99
105
.
2.
Khanafer
,
K.
,
Vafai
,
K.
, and
Lightstone
,
M.
,
2003
, “
Buoyancy-Driven Heat Transfer Enhancement in a Two-Dimensional Enclosure Utilizing Nanofluids
,”
Int. J. Heat Mass Transfer
,
46
(
19
), pp.
3639
3653
.
3.
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
.
4.
Buongiorno
,
J.
,
2006
, “
Convective Transport in Nanofluids
,”
ASME J. Heat Transfer
,
128
(
3
), pp.
240
250
.
5.
Rahman
,
M. M.
,
Roşca
,
A. V.
, and
Pop
,
I.
,
2014
, “
Boundary Layer Flow of a Nanofluid Past a Permeable Exponentially Shrinking Surface With Second Order Slip Using Buongiorno's Model
,”
Int. J. Heat Mass Transfer
,
77
, pp.
1133
1143
.
6.
Rahman
,
M. M.
,
Rosca
,
A. V.
, and
Pop
,
I.
,
2015
, “
Boundary Layer Flow of a Nanofluid Past a Permeable Exponentially Shrinking Surface With Convective Boundary Condition Using Buongiorno's Model
,”
Int. J. Numer. Meth. Heat Fluid Flow
,
25
(
2
), pp.
299
319
.
7.
Rahman
,
M. M.
,
Al-Rashdi
,
M. H.
, and
Pop
,
I.
,
2016
, “
Convective Boundary Layer Flow and Heat Transfer in a Nanofluid in the Presence of Second Order Slip, Constant Heat Flux and Zero Nanoparticles Flux
,”
Nucl. Eng. Des.
,
297
, pp.
95
103
.
8.
Rahman
,
M. M.
,
Al-Lawatia
,
M. A.
,
Eltayeb
,
I. A.
, and
Al-Salti
,
N.
,
2012
, “
Hydromagnetic Slip Flow of Water Based Nanofluids Past a Wedge With Convective Surface in the Presence of Heat Generation (or) Absorption
,”
Int. J. Therm. Sci
,
57
, pp.
172
182
.
9.
Rahman
,
M. M.
, and
Aziz
,
A.
,
2012
, “
Heat Transfer in Water Based Nanofluids (TiO2−H2O, Al2O3−H2O and Cu−H2O) Over a Stretching Cylinder
,”
Int. J. Heat Technol.
,
30
(
2
), pp.
43
49
.
10.
Rahman
,
M. M.
,
2016
, “
Influence of Oriented Magnetic Field on Natural Convection in an Equilateral Triangular Enclosure Filled With Water- and Kerosene-Based Ferrofluids Using a Two-Component Nonhomogeneous Thermal Equilibrium Model
,”
Cogent Phys.
,
3
(
1
), p.
123466
.
11.
Alsabery
,
A. I.
,
Sheremet
,
M. A.
,
Chamkha
,
A. J.
, and
Hashim
,
I.
,
2018
, “
Conjugate Natural Convection of Al2O3–Water Nanofluid in a Square Cavity With a Concentric Solid Insert Using Buongiorno's Two-Phase Model
,”
Int. J. Mech. Sci.
,
136
, pp.
200
219
.
12.
Uddin
,
M. J.
,
Kalbani
,
K. S.
,
Rahman
,
M. M.
,
Alam
,
M. S.
,
Al-Salti
,
N.
, and
Eltayeb
,
I. A.
,
2016
, “
Fundamentals of Nanofluids: Evolution, Applications and New Theory
,”
Int. J. Biomath. Sys. Biology
,
2
(
1
), pp.
1
32
.https://biomathsociety.in/issue2/paper4.pdf
13.
Rashidi
,
M. M.
,
Bég
,
O. A.
,
Asadi
,
M.
, and
Rastegari
,
M. T.
,
2011
, “
DTM-Padé Modeling of Natural Convective Boundary Layer Flow of a Nanofluid Past a Vertical Surface
,”
Int. J. Therm. Environ. Eng
,
4
(
1
), pp.
13
24
.
14.
Varol
,
Y.
,
Oztop
,
H. F.
, and
Pop
,
I.
,
2009
, “
Natural Convection in Right Angle Porous Trapezoidal Enclosure With Partially Cooled From Inclined Wall
,”
Int. Commun. Heat Mass Transfer
,
36
(
1
), pp.
6
15
.
15.
Das
,
S. K.
,
Choi
,
S. U. S.
,
Yu
,
W.
, and
Pradeep
,
Y.
,
2008
,
Nanofluids: Science and Technology
,
Wiley
,
Hoboken, NJ
.
16.
Nield
,
D. A.
, and
Bejan
,
A.
,
2013
,
Convection in Porous Media
,
4th ed.
,
Springer
,
New York
.
17.
Wong
,
K. V.
, and
Leon
,
O. D.
,
2010
, “
Applications of Nanofluids: Current and Future
,”
Adv. Mech. Eng.
,
2
, p.
519659
.
18.
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
.
19.
Kumar
,
V.
,
Tiwari
,
A. K.
, and
Ghosh
,
S. K.
,
2015
, “
Application of Nanofluids in Plate Heat Exchanger: A Review
,”
Energy Conver. Manage.
,
105
, pp.
1017
1036
.
20.
Wang
,
L.
, and
Fan
,
J.
,
2011
, “
Review of Heat Conduction in Nanofluids
,”
ASME J. Heat Transfer
,
133
(
4
), p.
040801
.
21.
Rahman
,
M. M.
,
Saghir
,
M. Z.
, and
Pop
,
I.
,
2019
, “
Steady Free Convection Flow Within a Titled Nanofluid Saturated Porous Cavity in the Presence of a Sloping Magnetic Field Energized by an Exothermic Chemical Reaction
,”
Int. J. Heat Mass Transfer
,
129
, pp.
198
211
.
22.
Chamkha
,
A. J.
,
Aziz
,
A.
, and
Ahmed
,
S. E.
,
2012
, “
Hydromagnetic Double-Diffusive Convection in a Rectangular Enclosure With Linearly Heated and Concentrated Wall (s) in the Presence of Heat Generation/Absorption Effects
,”
Prog. Comput. Fluid Dyn.
,
12
(
6
), pp.
400
414
.
23.
Chamkha
,
A. J.
, and
Al-Naser
,
H.
,
2002
, “
Hydromagnetic Double-Diffusive Convection in a Rectangular Enclosure With Uniform Side Heat and Mass Fluxes and Opposing Temperature and Concentration Gradients
,”
Int. J. Therm. Sci.
,
41
(
10
), pp.
936
948
.
24.
Chamkha
,
A. J.
, and
Ismael
,
M. A.
,
2014
, “
Natural Convection in Differentially Heated Partially Porous Layered Cavities Filled With a Nanofluid
,”
Numer. Heat Transfer, Part A
,
65
(
11
), pp.
1089
1113
.
25.
Nasrin
,
R.
,
Alim
,
M. A.
, and
Chamkha
,
A. J.
,
2012
, “
Combined Convection Flow in Triangular Wavy Chamber Filled With Water-CuO Nanofluid: Effect of Viscosity Models
,”
Int. Commun. Heat Mass
,
39
(
8
), pp.
1226
1236
.
26.
Ismael
,
M. A.
,
Armaghani
,
T.
, and
Chamkha
,
A. J.
,
2016
, “
Conjugate Heat Transfer and Entropy Generation in a Cavity Filled With a Nanofluid-Saturated Porous Media and Heated by a Triangular Solid
,”
J. Taiwan Inst. Chem. Eng.
,
59
, pp.
138
151
.
27.
Mansour
,
M. A.
,
Bakeir
,
M. A.
, and
Chamkha
,
A. J.
,
2014
, “
Natural Convection Inside a C-Shaped Nanofluid-Filled Enclosure With Localized Heat Sources
,”
Int. J. Numer. Method Heat Fluid Flow
,
24
(
8
), pp.
1954
1978
.
28.
Parvin
,
S.
, and
Chamkha
,
A. J.
,
2014
, “
An Analysis on Free Convection Flow, Heat Transfer and Entropy Generation in an Odd-Shaped Cavity Filled With Nanofluid
,”
Int. Commun. Heat Mass Transfer
,
54
, pp.
8
17
.
29.
Chamkha
,
A. J.
, and
Ismael
,
M. A.
,
2013
, “
Conjugate Heat Transfer in a Porous Cavity Filled With Nanofluids and Heated by a Triangular Thick Wall
,”
Int. J. Therm. Sci.
,
67
, pp.
135
151
.
30.
Ben-Cheikh
,
N.
,
Chamkha
,
A. J.
,
Ben-Beya
,
B.
, and
Lili
,
T.
,
2013
, “
Natural Convection of Water-Based Nanofluids in a Square Enclosure With Non-Uniform Heating of the Bottom Wall
,”
J. Moder. Phys.
,
04
(
02
), pp.
147
159
.
31.
Basak
,
T.
, and
Chamkha
,
A. J.
,
2012
, “
Heatline Analysis on Natural Convection for Nanofluids Confined Within Square Cavities With Various Thermal Boundary Conditions
,”
Int. J. Heat Mass Transfer
,
55
(
21–22
), pp.
5526
5543
.
32.
Selimefendigil
,
F.
,
Oztop
,
H. F.
, and
Chamkha
,
A. J.
,
2016
, “
MHD Mixed Convection and Entropy Generation of Nanofluid Filled Lid Driven Cavity Under the Influence of Inclined Magnetic Fields Imposed to Its Upper and Lower Diagonal Triangular Domains
,”
J. Magn. Magn. Mater.
,
406
, pp.
266
281
.
33.
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
, pp.
751
761
.
34.
Rahman
,
M. M.
,
Alam
,
M. S.
,
Al-Salti
,
N.
, and
Eltayeb
,
I. A.
,
2016
, “
Hydromagnetic Natural Convective Heat Transfer Flow in an Isosceles Triangular Cavity Filled With Nanofluid Using Two-Component Nonhomogeneous Model
,”
Int. J. Therm. Sci.
,
107
, pp.
272
288
.
35.
Astanina
,
M. S.
,
Riahi
,
M. K.
,
Abu-Nada
,
E.
, and
Sheremet
,
M. A.
,
2018
, “
Magnetohydrodynamic in Partially Heated Square Cavity With Variable Properties: Discrepancy in Experimental and Theoretical Conductivity Correlations
,”
Int. J. Heat Mass Transfer
,
116
, pp.
532
548
.
36.
Pordanjani
,
A. H.
,
Jahanbakhshi
,
A.
,
Nadooshan
,
A. A.
, and
Afrand
,
M.
,
2018
, “
Effect of Two Isothermal Obstacles on the Natural Convection of Nanofluid in the Presence of Magnetic Field Inside an Enclosure With Sinusoidal Wall Temperature Distribution
,”
Int. J. Heat Mass Transfer
,
121
, pp.
565
578
.
37.
Uddin
,
M. J.
, and
Rahman
,
M. M.
,
2018
, “
Finite Element Computational Procedure for Convective Flow of Nanofluids in an Annulus
,”
Therm. Sci. Eng. Prog.
,
6
, pp.
251
267
.
38.
Uddin
,
M. J.
,
Rahman
,
M. M.
, and
Alam
,
M. S.
,
2018
, “
Analysis of Natural Convective Heat Transport in Homocentric Annuli Containing Nanofluids With an Oriented Magnetic Field Using Nonhomogeneous Dynamic Model
,”
Neural Comput. Appl.
,
30
(
10
), pp.
3189
3208
.
39.
Uddin
,
M. J.
,
Alam
,
M. S.
, and
Rahman
,
M. M.
,
2017
, “
Natural Convective Heat Transfer Flow of Nanofluids Inside a Quarter-Circular Enclosure Using Nonhomogeneous Dynamic Model
,”
Arab. J. Sci. Eng.
,
42
(
5
), pp.
1883
1901
.
40.
Uddin
,
M. J.
,
Alam
,
M. S.
,
Al-Salti
,
N.
, and
Rahman
,
M. M.
,
2016
, “
Investigations of Natural Convection Heat Transfer in Nanofluids Filled Horizontal Semicircular-Annulus Using Nonhomogeneous Dynamic Model
,”
Am. J. Heat Mass Transfer
,
3
(
6
), pp.
425
452
.
41.
Al-Balushi
,
L. M.
,
Uddin
,
M. J.
, and
Rahman
,
M. M.
,
2018
, “
Natural Convective Heat Transfer in a Square Enclosure Utilizing Magnetic Nanoparticles
,”
Propul. Power Res.
(epub).
42.
Maxwell
,
J. C.
,
1878
, “
On Stresses in Rarefied Gases Arising From Inequalities of Temperature
,”
Proc. R. Soc. London
,
27
, pp.
185
189
.
43.
Hamilton
,
R. L.
, and
Crosser
,
O. K.
,
1962
, “
Thermal Conductivity of Heterogeneous Two Component Systems
,”
Ind. Eng. Chem. Fund.
,
1
(
3
), pp.
187
191
.
44.
Xuan
,
Y.
,
Li
,
Q.
, and
Hu
,
W.
,
2003
, “
Aggregation Structure and Thermal Conductivity of Nanofluids
,”
AIChE J.
,
49
(
4
), pp.
1038
1043
.
45.
Hafezisefat
,
P.
,
Esfahany
,
M. N.
, and
Jafari
,
M.
,
2017
, “
An Experimental and Numerical Study of Heat Transfer in Jacketed Vessels by SiO2 Nanofluid
,”
Heat Mass Transfer
,
53
(
7
), pp.
2395
2405
.
46.
Khan
,
W. A.
,
Khan
,
Z. H.
, and
Haq
,
R. U.
,
2015
, “
Flow and Heat Transfer of Ferrofluids Over a Flat Plate With Uniform Heat Flux
,”
Eur. Phys. J. Plus
,
130
(
4
), p.
86
.
47.
Zienkiewicz
,
O. C.
, and
Taylor
,
R. L.
,
2000
,
Finite Element Method: Vol. 3: Fluid Dynamics
,
Elsevier Science & Technology Books
,
Cambridge, MA
.
48.
Al Kalbani
,
K. S.
,
Alam
,
M. S.
, and
Rahman
,
M. M.
,
2016
, “
Finite Element Analysis of Unsteady Natural Convective Heat Transfer and Fluid Flow of Nanofluids Inside a Tilted Square Enclosure in the Presence of Oriented Magnetic Field
,”
Am. J. Heat Mass Transfer
,
3
(
3
), pp.
186
224
.
49.
Barakos
,
G.
,
Mitsoulis
,
E.
, and
Assimacopoulos
,
D.
,
1994
, “
Natural Convection Flow in a Square Cavity Revisited: Laminar and Turbulent Models With Wall Functions
,”
Int. J. Numer. Meth. Heat Fluid Flow
,
18
(
7
), pp.
695
719
.
50.
Fusegi
,
T.
,
Hyun
,
J. M.
,
Kuwahara
,
K.
, and
Farouk
,
B.
,
1991
, “
A Numerical Study of Three-Dimensional Natural Convection in a Differentially Heated Cubical Enclosure
,”
Int. J. Heat Mass Transfer
,
34
(
6
), pp.
1543
1557
.
You do not currently have access to this content.