In this study, free convection in a cavity with differentially heated wavy walls is numerically investigated in the presence of a magnetic source. Polyharmonic spline radial basis function (RBF) is utilized to discretize the governing dimensionless equations formulated by stream function-vorticity. The effects of dimensionless Hartmann number, Rayleigh number, the number of undulations, amplitude of wave, and the location of magnetic source are visualized in streamlines and isotherms as well as calculating average Nusselt number through the heated wall. Results show that primary vortex in streamlines is altered with the impact of magnetic source. The augmentation of undulations and amplitude causes convective heat transfer to decrease if Ra = 105. The impact of location of magnetic source is noted close to the top wall.

References

References
1.
Al-Amiri
,
A.
,
Khanafer
,
K.
,
Bull
,
J.
, and
Pop
,
I.
,
2007
, “
Effect of Sinusoidal Wavy Bottom Surface on Mixed Convection Heat Transfer in a Lid-Driven Cavity
,”
Int. J. Heat Mass Transfer
,
50
(
9–10
), pp.
1771
1780
.
2.
Abu-Nada
,
E.
, and
Oztop
,
H. F.
,
2011
, “
Numerical Analysis of Al2O3/Water Nanofluids Natural Convection in a Wavy Walled Cavity
,”
Numer. Heat Transfer, Part A
,
59
(
5
), pp.
403
419
.
3.
Esmaeilpour
,
M.
, and
Abdollahzadeh
,
M.
,
2012
, “
Free Convection and Entropy Generation of Nanofluid Inside an Enclosure With Different Patterns of Vertical Wavy Walls
,”
Int. J. Therm. Sci.
,
52
, pp.
127
136
.
4.
Sheikholeslami
,
M.
, and
Chamkha
,
A. J.
,
2016
, “
Electrohydrodynamic Free Convection Heat Transfer of a Nanofluid in a Semi-Annulus Enclosure With a Sinusoidal Wall
,”
Numer. Heat Transfer, Part A
,
69
(
7
), pp.
781
793
.
5.
Shehzad
,
N.
,
Zeeshan
,
A.
,
Ellahi
,
R.
, and
Vafai
,
K.
,
2016
, “
Convective Heat Transfer of Nanofluid in a Wavy Channel: Buongiorno's Mathematical Model
,”
J. Mol. Liq.
,
222
, pp.
446
455
.
6.
Sheremet
,
M. A.
,
Revnic
,
C.
, and
Pop
,
I.
,
2017
, “
Free Convection in a Porous Wavy Cavity Filled With a Nanofluid Using Buongiorno's Mathematical Model With Thermal Dispersion Effect
,”
Appl. Math. Comput.
,
299
, pp.
1
15
.
7.
Sheremet
,
M. A.
,
Pop
,
I.
, and
Ishak
,
A.
,
2017
, “
Time-Dependent Natural Convection of Micropolar Fluid in a Wavy Triangular Cavity
,”
Int. J. Heat Mass Transfer
,
105
, pp.
610
622
.
8.
Sheremet
,
M. A.
,
Cimpean
,
D. S.
, and
Pop
,
I.
,
2017
, “
Free Convection in a Partially Heated Wavy Porous Cavity Filled With a Nanofluid Under the Effects of Brownian Diffusion and Thermophoresis
,”
Appl. Therm. Eng.
,
113
, pp.
413
418
.
9.
Cheong
,
H. T.
,
Sivasankaran
,
S.
, and
Bhuvaneswari
,
M.
,
2017
, “
Natural Convection in a Wavy Porous Cavity With Sinusoidal Heating and Internal Heat Generation
,”
Int. J. Numer. Meth Heat Fluid Flow
,
27
(
2
), pp.
287
309
.
10.
Cheong
,
H. T.
,
Sivasankaran
,
S.
, and
Bhuvaneswari
,
M.
,
2018
, “
Effect of Aspect Ratio on Natural Convection in a Porous Wavy Cavity
,”
Arabian J. Sci. Eng.
,
43
(
3
), pp.
1409
1421
.
11.
Segunda
,
V. M.
,
Ormiston
,
S. J.
, and
Tachie
,
M. F.
,
2018
, “
Experimental and Numerical Investigation of Developing Turbulent Flow Over a Wavy Wall in a Horizontal Channel
,”
Eur. J. Mech.-B
,
68
, pp.
128
143
.
12.
Haq
,
R.
,
Soomro
,
F. A.
,
Mekkaoui
,
T.
, and
Al-Mdallal
,
Q. M.
,
2018
, “
MHD Natural Convection Flow in a Corrugated Cavity Filled With a Porous Medium
,”
Int. J. Heat Mass Transfer
,
121
, pp.
1168
1178
.
13.
Roy
,
N. C.
,
2018
, “
Modelling of a Closed Two-Dimensional Reactor Bounded by a Wavy Wall
,”
J. Combust. Theory Modell.
,
22
(4), pp. 666–693.
14.
Adjlout
,
L.
,
Imine
,
O.
,
Azzi
,
A.
, and
Belkadi
,
M.
,
2002
, “
Laminar Natural Convection in an Inclined Cavity With a Wavy Wall
,”
Int. J. Heat Mass Transfer
,
45
(
10
), pp.
2141
2152
.
15.
Das
,
P. K.
, and
Mahmud
,
S.
,
2003
, “
Numerical Investigation of Natural Convection Inside a Wavy Enclosure
,”
Int. J. Therm. Sci.
,
42
(
4
), pp.
397
406
.
16.
Mahmud
,
S.
,
Das
,
P. K.
,
Hyder
,
N.
, and
Islam
,
A. K. M.
,
2002
, “
Free Convection in an Enclosure With Vertical Wavy Walls
,”
Int. J. Therm. Sci.
,
41
(
5
), pp.
440
446
.
17.
Rostami
,
J.
,
2008
, “
Unsteady Natural Convection in an Enclosure With Vertical Wavy Walls
,”
Heat Mass Transfer
,
44
(
9
), pp.
1079
1087
.
18.
Oztop
,
H. F.
,
Sakhrieh
,
A.
,
Abu-Nada
,
E.
, and
Al-Salem
,
K.
,
2017
, “
Mixed Convection of MHD Flow in Nanofluid Filled and Partially Heated Wavy Walled Lid-Driven Enclosure
,”
Int. Commun. Heat Mass Transfer
,
86
, pp.
42
51
.
19.
Alsabery
,
A. I.
,
Tayebi
,
T.
,
Chamkha
,
A. J.
, and
Hashim
,
I.
,
2018
, “
Effect of Rotating Solid Cylinder on Entropy Generation and Convective Heat Transfer in a Wavy Porous Cavity Heated From Below
,”
Int. Commun. Heat Mass Transfer
,
95
, pp.
197
209
.
20.
Ashorynejad
,
H. R.
, and
Shahriari
,
A.
,
2018
, “
MHD Natural Convection of Hybrid Nanofluid in an Open Wavy Cavity
,”
Results Phys.
,
9
, pp.
440
455
.
21.
Misirlioglu
,
A.
,
Baytas
,
A. C.
, and
Pop
,
I.
,
2005
, “
Free Convection in a Wavy Cavity Filled With a Porous Medium
,”
Int. J. Heat Mass Transfer
,
48
(
9
), pp.
1840
1850
.
22.
Hatami
,
M.
,
2017
, “
Nanoparticles Migration Around the Heated Cylinder During the RSM Optimization of a Wavy-Wall Enclosure
,”
Adv. Powder Technol.
,
28
(
3
), pp.
890
899
.
23.
Mosayebidorcheh
,
S.
, and
Hatami
,
M.
,
2018
, “
Analytical Investigation of Peristaltic Nanofluid Flow and Heat Transfer in an Asymmetric Wavy Wall Channel—Part I: Straight Channel
,”
Int. J. Heat Mass Transfer
,
126
, pp.
790
799
.
24.
Mosayebidorcheh
,
S.
, and
Hatami
,
M.
,
2018
, “
Analytical Investigation of Peristaltic Nanofluid Flow and Heat Transfer in an Asymmetric Wavy Wall Channel—Part II: Divergent Channel
,”
Int. J. Heat Mass Transfer
,
126
, pp.
800
808
.
25.
Rashidi
,
S.
,
Akbarzadeh
,
M.
,
Masoodi
,
R.
, and
Languri
,
E. M.
,
2017
, “
Thermal-Hydraulic and Entropy Generation Analysis for Turbulent Flow Inside Corrugated Channel
,”
Int. J. Heat Mass Transfer
,
109
, pp.
812
823
.
26.
Akbarzadeh
,
M.
, and
Maghrebi
,
M. J.
,
2018
, “
Combined Effects of Corrugated Walls and Porous Inserts on Performance Improvement in a Heat Exchanger Channel
,”
Int. J. Therm. Sci.
,
127
, pp.
266
276
.
27.
Tang
,
W.
,
Hatami
,
M.
,
Zhou
,
J.
, and
Jing
,
D.
,
2017
, “
Natural Convection Heat Transfer in a Nanofluid-Filled Cavity With Double Sinusoidal Wavy Walls of Various Phase Deviations
,”
Int. J. Heat Mass Transfer
,
115
, pp.
430
440
.
28.
Pekmen Geridonmez
,
B.
,
2016
, “
RBF Simulation of Natural Convection in a Nanofluid-Filled Cavity
,”
AIMS Math.
,
1
(
3
), pp.
195
207
.
29.
Pekmen Geridonmez
,
B.
,
2018
, “
Numerical Simulation of Natural Convection in a Porous Cavity Filled With Ferrofluid in Presence of Magnetic Source
,”
J. Therm. Eng.
,
4
(2), pp. 1756–1769.
30.
Pekmen Geridonmez
,
B.
,
2018
, “
Numerical Investigation of Ferrofluid Convection With Kelvin Forces and Non-Darcy Effects
,”
AIMS Math.
,
3
, pp.
195
210
.
31.
Tzirtzilakis
,
E. E.
, and
Xenos
,
M. A.
,
2013
, “
Biomagnetic Fluid Flow in Driven Cavity
,”
Meccanica
,
48
(
1
), pp.
187
200
.
32.
Fasshauer
,
G. E.
,
2007
,
Meshfree Approximation Methods With Matlab
,
World Scientific Publications
,
Singapore
.
33.
Fasshauer
,
G. E.
, and
McCourt
,
M.
,
2015
,
Kernel-based Approximation Methods Using MATLAB
,
World Scientific Publications
,
Singapore
.
34.
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
.
You do not currently have access to this content.