In this paper, the effect of magnetic field on natural convection of Al2O3/water nanofluid in an enclosure containing twin protruding heat sources placed on top and bottom walls arranged in-line and staggered manner is presented. For this purpose, coupled equations governing fluid flow and heat transfer are solved in Cartesian framework using streamline upwind/Petrov–Galerkin (SUPG) finite element method. Numerical computations are performed to predict the fluid flow, heat transfer, and entropy generation for a wide range of Hartmann number (0.0 $≤$ Ha $≤$ 100.0), Rayleigh number ($103≤Ra≤106$), and nanoparticle volume fraction ($0.0≤ϕ≤0.1$). The simulated results indicate that, for both in-line and staggered arrangement, the entropy generation due to heat transfer is significant along isothermal surfaces, whereas entropy generation due to fluid friction is higher at no-slip walls and along the regions of contact between adjacent recirculation cells. For both in-line and staggered arrangement, increase in global total entropy generation and average Nusselt number along top and bottom heat sources is obtained with decreasing Ha and increasing Ra. Furthermore, for both in-line and staggered arrangement, variation in global total entropy generation and average Nusselt number along top and bottom heat sources with increasing nanoparticle volume fraction, depend on both Ha and Ra.

## References

References
1.
Sparrow
,
E.
, and
Cess
,
R.
,
1961
, “
The Effect of a Magnetic Field on Free Convection Heat Transfer
,”
Int. J. Heat Mass Transfer
,
3
(
4
), pp.
267
274
.
2.
Rudraiah
,
N.
,
Barron
,
R.
,
Venkatachalappa
,
M.
, and
Subbaraya
,
C.
,
1995
, “
Effect of a Magnetic Field on Free Convection in a Rectangular Enclosure
,”
Int. J. Eng. Sci.
,
33
(
8
), pp.
1075
1084
.
3.
Sathiyamoorthy
,
M.
, and
Chamkha
,
A.
,
2010
, “
Effect of Magnetic Field on Natural Convection Flow in a Liquid Gallium Filled Square Cavity for Linearly Heated Side Wall(s)
,”
Int. J. Therm. Sci.
,
49
(
9
), pp.
1856
1865
.
4.
Choi
,
S. U.
, and
Eastman
,
J.
,
1995
, “
Enhancing Thermal Conductivity of Fluids With Nanoparticles
,” Argonne National Laboratory, Lemont, IL,
Technical Report No. ANL/MSD/CP--84938
.
5.
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
.
6.
Anilkumar
,
S.
, and
Kuzhiveli
,
B. T.
,
2009
, “
Numerical Study of Natural Convective Heat Transfer in a Two-Dimensional Cavity With Centrally Located Partition Utilizing Nanofluids
,”
ASME J. Therm. Sci. Eng. Appl.
,
1
(
3
), p.
031004
.
7.
Ho
,
C.
,
Liu
,
W.
,
Chang
,
Y.
, and
Lin
,
C.
,
2010
, “
Natural Convection Heat Transfer of Alumina-Water Nanofluid in Vertical Square Enclosures: An Experimental Study
,”
Int. J. Therm. Sci.
,
49
(
8
), pp.
1345
1353
.
8.
Tayebi
,
T.
,
Chamkha
,
A. J.
,
Djezzar
,
M.
, and
Bouzerzour
,
A.
,
2016
, “
Natural Convective Nanofluid Flow in an Annular Space Between Confocal Elliptic Cylinders
,”
ASME J. Therm. Sci. Eng. Appl.
,
9
(
1
), p.
011010
.
9.
Bouhalleb
,
M.
, and
Abbassi
,
H.
,
2016
, “
Numerical Investigation of Heat Transfer by CuO-Water Nanofluid in Rectangular Enclosures
,”
Heat Transfer Eng.
,
37
(
1
), pp.
13
23
.
10.
Putra
,
N.
,
Roetzel
,
W.
, and
Das
,
S.
,
2003
, “
Natural Convection of Nano-Fluids
,”
Heat Mass Transfer
,
39
(
8–9
), pp.
775
784
.
11.
Ternik
,
P.
,
2015
, “
Conduction and Convection Heat Transfer Characteristics of Water-Au Nanofluid in a Cubic Enclosure With Differentially Heated Side Walls
,”
Int. J. Heat Mass Transfer
,
80
, pp.
368
375
.
12.
,
H.
,
Sharifpur
,
M.
, and
Meyer
,
J. P.
,
2016
, “
Experimental Investigation on Cavity Flow Natural Convection of Al2O3 Water Nanofluids
,”
Int. Commun. Heat Mass Transfer
,
76
, pp.
316
324
.
13.
Ghasemi
,
B.
,
,
S.
, and
Raisi
,
A.
,
2011
, “
Magnetic Field Effect on Natural Convection in a Nanofluid-Filled Square Enclosure
,”
Int. J. Therm. Sci.
,
50
(
9
), pp.
1748
1756
.
14.
Mahmoudi
,
A. H.
,
Pop
,
I.
,
Shahi
,
M.
, and
Talebi
,
F.
,
2013
, “
MHD Natural Convection and Entropy Generation in a Trapezoidal Enclosure Using Cu-Water Nanofluid
,”
Comput. Fluids
,
72
, pp.
46
62
.
15.
Mejri
,
I.
, and
Mahmoudi
,
A.
,
2015
, “
MHD Natural Convection in a Nanofluid-Filled Open Enclosure With a Sinusoidal Boundary Condition
,”
Chem. Eng. Res. Des.
,
98
, pp.
1
16
.
16.
Mahmoudi
,
A. H.
,
Shahi
,
M.
,
Shahedin
,
A. M.
, and
Hemati
,
N.
,
2011
, “
Numerical Modeling of Natural Convection in an Open Cavity With Two Vertical Thin Heat Sources Subjected to a Nanofluid
,”
Int. Commun. Heat Mass Transfer
,
38
(
1
), pp.
110
118
.
17.
,
S.
, and
Ghasemi
,
B.
,
2011
, “
Natural Convection of Water-CuO Nanofluid in a Cavity With Two Pairs of Heat Source-Sink
,”
Int. Commun. Heat Mass Transfer
,
38
(
5
), pp.
672
678
.
18.
Mahmoudi
,
A. H.
,
Pop
,
I.
, and
Shahi
,
M.
,
2012
, “
Effect of Magnetic Field on Natural Convection in a Triangular Enclosure Filled With Nanofluid
,”
Int. J. Therm. Sci.
,
59
, pp.
126
140
.
19.
Lam
,
P. A. K.
, and
Prakash
,
K. A.
,
2014
, “
A Numerical Study on Natural Convection and Entropy Generation in a Porous Enclosure With Heat Sources
,”
Int. J. Heat Mass Transfer
,
69
, pp.
390
407
.
20.
Brooks
,
A. N.
, and
Hughes
,
T. J. R.
,
1982
, “
Streamline Upwind/Petrov–Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier–Stokes Equations
,”
Comput. Methods Appl. Mech. Eng.
,
32
(
1–3
), pp.
199
259
.
21.
Prakash
,
K.
,
Biswas
,
G.
, and
Kumar
,
B.
,
2007
, “
Numerical Prediction of Fluid Flow and Heat Transfer in the Target System of an Axisymmetric Accelerator-Driven Subcritical System
,”
J. Heat Transfer
,
129
(
4
), pp.
582
588
.
22.
Lam
,
P. A. K.
, and
Prakash
,
K. A.
,
2015
, “
A Numerical Investigation of Heat Transfer and Entropy Generation During Jet Impingement Cooling of Protruding Heat Sources Without and With Porous Medium
,”
Energy Convers. Manage.
,
89
, pp.
626
643
.
23.
Lam
,
P. A. K.
, and
Prakash
,
K. A.
,
2016
, “
Thermodynamic Investigation and Multi-Objective Optimization for Jet Impingement Cooling System With Al2O3/Water Nanofluid
,”
Energy Convers. Manage.
,
111
, pp.
38
56
.