Abstract

For the very first time, this study attempts to address the heat dissipation from an isothermal ribbed sphere under the action of pure natural convection. Semicircular ribs of different radii are superimposed azimuthally on the outer surface of a sphere. The addition of ribs on the sphere serves a dual purpose in its practical applications: beautification of electronic devices such as spherical light sources as well as an increase in heat dissipation from the hot surface, which prevents the electronic component from getting overheated. Finite volume method-based axisymmetric numerical simulations are performed in the laminar flow regime for the following ranges of nondimensional parameters: Rayleigh number (102 ≤ Ra ≤ 108), inter-rib-spacing to sphere diameter (0.191 ≤ P/D ≤ 0.785), and rib-radius to sphere diameter (0.03 ≤ R/D ≤ 0.083). The main target of this study is to identify the critical parameters for heat transfer enhancement from the ribbed sphere compared to a conventional plane sphere. The results obtained from this work show that the average Nusselt number increases with an increase in Ra and P/D, whereas it decreases as R/D increases. Effectiveness of the ribs (εrib) and critical Rayleigh numbers (Racr), corresponding to εrib = 1, are also calculated. Ribs are more effective in heat dissipation at low Ra and P/D and high R/D. A correlation for the average Nusselt number is also developed in this work, which would help design a better thermal management system.

References

1.
Liu
,
T. Y.
,
Campbell
,
A. N.
,
Cardoso
,
S. S. S.
, and
Hayhurst
,
A. N.
,
2008
, “
Effects of Natural Convection on Thermal Explosion in a Closed Vessel
,”
Phys. Chem. Chem. Phys.
,
10
(
36
), pp.
5521
5530
.10.1039/b808222g
2.
Yang
,
L.
,
Zhang
,
X.
, and
Xu
,
G.
,
2014
, “
Thermal Performance of a Solar Storage Packed Bed Using Spherical Capsules Filled With PCM Having Different Melting Points
,”
Energy Build.
,
68
(
Part B
), pp.
639
646
.10.1016/j.enbuild.2013.09.045
3.
Verwey
,
C.
, and
Birouk
,
M.
,
2018
, “
Experimental Investigation of the Effect of Natural Convection on the Evaporation Characteristics of Small Fuel Droplets at Moderately Elevated Temperature and Pressure
,”
Int. J. Heat Mass Transfer
,
118
, pp.
1046
1055
.10.1016/j.ijheatmasstransfer.2017.11.038
4.
Singh
,
S. N.
, and
Chen
,
J.
,
1980
, “
Numerical Solution for Free Convection Between Concentric Spheres at Moderate Grashof Numbers
,”
Numer. Heat Transfer
,
3
(
4
), pp.
441
459
.10.1080/01495728008961770
5.
Biradar
,
B. A.
,
Rath
,
S.
, and
Dash
,
S. K.
,
2021
, “
Orientation Effects on Conjugate Natural Convection Heat Transfer From an LED Bulb: A Numerical Study
,”
Int. J. Therm. Sci.
,
159
, p.
106640
.10.1016/j.ijthermalsci.2020.106640
6.
Baïri
,
A.
,
Alilat
,
N.
, and
Déniz Quintana
,
F.
,
2020
, “
Experimental Study of Free Convective Heat Transfer Around a Spherical Electronic Component Cooled by Means of Porous Media Saturated by Nanofluid
,”
Heat Mass Transfer
,
56
(
11
), pp.
3085
3092
.10.1007/s00231-020-02908-8
7.
Elenbaas
,
W.
,
1942
, “
The Dissipation of Heat by Free Convection of Spheres and Horizontal Cylinders
,”
Physics
,
9
(
3
), pp.
285
296
.10.1016/S0031-8914(42)90111-3
8.
Chiang
,
T.
,
Ossin
,
A.
, and
Tien
,
C. L.
,
1964
, “
Laminar Free Convection From a Sphere
,”
ASME J. Heat Transfer-Trans. ASME
,
86
(
4
), pp.
537
541
.10.1115/1.3688739
9.
Amato
,
W. S.
, and
Chi
,
T.
,
1972
, “
Free Convection Heat Transfer From Isothermal Spheres in Water
,”
Int. J. Heat Mass Transfer
,
15
(
2
), pp.
327
339
.10.1016/0017-9310(72)90078-6
10.
Kitamura
,
K.
,
Mitsuishi
,
A.
,
Suzuki
,
T.
, and
Misumi
,
T.
,
2015
, “
Fluid Flow and Heat Transfer of High-Rayleigh-Number Natural Convection Around Heated Spheres
,”
Int. J. Heat Mass Transfer
,
86
, pp.
149
157
.10.1016/j.ijheatmasstransfer.2015.02.081
11.
Mathers
,
W. G.
,
Madden
,
A. J.
, and
Piret
,
E. L.
,
1957
, “
Simultaneous Heat and Mass Transfer in Free Convection
,”
Ind. Eng. Chem.
,
49
(
6
), pp.
961
968
.10.1021/ie50570a025
12.
Churchill
,
S. W.
,
1983
, “
Comprehensive, Theoretically Based, Correlating Equations for Free Convection From Isothermal Spheres
,”
Chem. Eng. Commun.
,
24
(
4–6
), pp.
339
352
.10.1080/00986448308940090
13.
Jafarpur
,
K.
, and
Yovanovich
,
M. M.
,
1992
, “
Laminar Free Convective Heat Transfer From Isothermal Spheres: A New Analytical Method
,”
Int. J. Heat Mass Transfer
,
35
(
9
), pp.
2195
2201
.10.1016/0017-9310(92)90063-X
14.
Potter
,
J. M.
, and
Riley
,
N.
,
1980
, “
Free Convection From a Heated Sphere at Large Grashof Number
,”
J. Fluid Mech.
,
100
(
4
), pp.
769
783
.10.1017/S0022112080001395
15.
Geoola
,
F.
, and
Cornish
,
A. R. H.
,
1981
, “
Numerical Solution of Steady-State Free Convective Heat Transfer From a Solid Sphere
,”
Int. J. Heat Mass Transfer
,
24
(
8
), pp.
1369
1379
.10.1016/0017-9310(81)90187-3
16.
Fujii
,
T.
,
Fujii
,
M.
, and
Honda
,
T.
,
1981
, “
A Numerical Analysis of Laminar Free Convection Around an Isothermal Sphere
,”
Numer. Heat Transfer
,
4
(
1
), pp.
69
84
.10.1080/01495728108961779
17.
Jia
,
H.
, and
Gogos
,
G.
,
1996
, “
Laminar Natural Convection Heat Transfer From Isothermal Spheres
,”
Int. J. Heat Mass Transfer
,
39
(
8
), pp.
1603
1615
.10.1016/0017-9310(95)00259-6
18.
Jia
,
H.
, and
Gogos
,
G.
,
1996
, “
Transient Laminar Natural Convection Heat Transfer From Isothermal Spheres
,”
Numer. Heat Transfer Part A Appl.
,
29
(
1
), pp.
83
101
.10.1080/10407789608913780
19.
Yang
,
S.
,
Raghavan
,
V.
, and
Gogos
,
G.
,
2007
, “
Numerical Study of Transient Laminar Natural Convection Over an Isothermal Sphere
,”
Int. J. Heat Fluid Flow
,
28
(
4
), pp.
821
837
.10.1016/j.ijheatfluidflow.2006.08.004
20.
Prhashanna
,
A.
, and
Chhabra
,
R. P.
,
2010
, “
Free Convection in Power-Law Fluids From a Heated Sphere
,”
Chem. Eng. Sci.
,
65
(
23
), pp.
6190
6205
.10.1016/j.ces.2010.09.003
21.
Abdulateef
,
A. M.
,
Mat
,
S.
,
Abdulateef
,
J.
,
Sopian
,
K.
, and
Al-Abidi
,
A. A.
,
2018
, “
Geometric and Design Parameters of Fins Employed for Enhancing Thermal Energy Storage Systems: A Review
,”
Renewable Sustainable Energy Rev.
,
82
, pp.
1620
1635
.10.1016/j.rser.2017.07.009
22.
Niculin
,
D.
,
Strelets
,
M.
,
Dvinsky
,
A.
, and
Bar-Cohen
,
A.
,
1996
, “
Navier-Stokes Study of Natural Convection and Heat Transfer in Vertical Symmetrically Heated Plate-Fin Heat Sinks
,”
Numer. Heat Transfer Part A Appl.
,
30
(
7
), pp.
703
720
.10.1080/10407789608913866
23.
Tari
,
I.
, and
Mehrtash
,
M.
,
2013
, “
Natural Convection Heat Transfer From Inclined Plate-Fin Heat Sinks
,”
Int. J. Heat Mass Transfer
,
56
(
1–2
), pp.
574
593
.10.1016/j.ijheatmasstransfer.2012.08.050
24.
Sundar
,
S.
,
Song
,
G.
,
Zahir
,
M. Z.
,
Jayakumar
,
J. S.
, and
Yook
,
S. J.
,
2019
, “
Performance Investigation of Radial Heat Sink With Circular Base and Perforated Staggered Fins
,”
Int. J. Heat Mass Transfer
,
143
, p.
118526
.10.1016/j.ijheatmasstransfer.2019.118526
25.
Karlapalem
,
V.
,
Rath
,
S.
, and
Dash
,
S. K.
,
2019
, “
Orientation Effects on Laminar Natural Convection Heat Transfer From Branching-Fins
,”
Int. J. Therm. Sci.
,
142
, pp.
89
105
.10.1016/j.ijthermalsci.2019.04.007
26.
Yildiz
,
S.
, and
Yüncü
,
H.
,
2004
, “
An Experimental Investigation on Performance of Annular Fins on a Horizontal Cylinder in Free Convection Heat Transfer
,”
Heat Mass Transfer
,
40
(
3–4
), pp.
239
251
.10.1007/s00231-002-0404-x
27.
Senapati
,
J. R.
,
Dash
,
S. K.
, and
Roy
,
S.
,
2017
, “
Numerical Investigation of Natural Convection Heat Transfer From Vertical Cylinder With Annular Fi Ns
,”
Int. J. Therm. Sci.
,
111
, pp.
146
159
.10.1016/j.ijthermalsci.2016.08.019
28.
Shen
,
Q.
,
Sun
,
D.
,
Xu
,
Y.
,
Jin
,
T.
,
Zhao
,
X.
,
Zhang
,
N.
,
Wu
,
K.
, and
Huang
,
Z.
,
2016
, “
Natural Convection Heat Transfer Along Vertical Cylinder Heat Sinks With Longitudinal Fins
,”
Int. J. Therm. Sci.
,
100
, pp.
457
464
.10.1016/j.ijthermalsci.2015.09.007
29.
Acharya
,
S.
, and
Dash
,
S. K.
,
2018
, “
Natural Convection Heat Transfer From a Hollow Horizontal Cylinder With External Longitudinal Fins: A Numerical Approach
,”
Numer. Heat Transfer Part A Appl.
,
74
(
7
), pp.
1405
1423
.10.1080/10407782.2018.1505096
30.
Anderson
,
D. E.
,
Truslove
,
T. E.
, and
Kubie
,
J.
,
2003
, “
Thermal Modelling and Optimization of Heat Transfer in a High-Temperature Theatre Luminaire
,”
Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
,
217
(
9
), pp.
1039
1048
.10.1243/095440603322407272
31.
Yu
,
G.-y.
,
Zhu
,
X.-P.
,
Hu
,
S.-h.
,
Hao
,
W.-W.
, and
Guo
,
T.-T.
,
2011
, “
Thermal Simulation and Optimization Design on a High- Power LED Spot Lamp
,”
Optoelectron. Lett.
,
7
(
2
), pp.
117
121
.10.1007/s11801-011-0142-8
32.
Maaspuro
,
M.
, and
Tuominen
,
A.
,
2013
, “
Thermal Analysis of LED Spot Lighting Device Operating in External Natural or Forced Heat Convection
,”
Microelectron. Reliab.
,
53
(
3
), pp.
428
434
.10.1016/j.microrel.2012.10.004
33.
Singh
,
B.
, and
Dash
,
S. K.
,
2015
, “
Natural Convection Heat Transfer From a Finned Sphere
,”
Int. J. Heat Mass Transfer
,
81
, pp.
305
324
.10.1016/j.ijheatmasstransfer.2014.10.028
34.
Rath
,
S.
, and
Dash
,
S. K.
,
2020
, “
Numerical Study of Laminar and Turbulent Natural Convection From a Stack of Solid Horizontal Cylinders
,”
Int. J. Therm. Sci.
,
148
, p.
106147
.10.1016/j.ijthermalsci.2019.106147
35.
ANSYS
,
2013
,
ANSYS Fluent Release 15.0 User Manual
,
ANSYS
,
Canonsburg, PA
.
36.
Rath
,
S.
, and
Dash
,
S. K.
,
2019
, “
Numerical Investigation of Natural Convection Heat Transfer From a Stack of Horizontal Cylinders
,”
ASME J. Heat Transfer-Trans. ASME
,
141
(
1
), p.
012501
.10.1115/1.4040954
37.
Rath
,
S.
, and
Dash
,
S. K.
,
2019
, “
Laminar and Turbulent Natural Convection From a Stack of Thin Hollow Horizontal Cylinders: A Numerical Study
,”
Numer. Heat Transfer Part A Appl.
,
75
(
11
), pp.
753
775
.10.1080/10407782.2019.1608776
38.
Rath
,
S.
, and
Dash
,
S. K.
,
2019
, “
Effect of Horizontal Spacing and Tilt Angle on Thermo-Buoyant Natural Convection From Two Horizontally Aligned Square Cylinders
,”
Int. J. Therm. Sci.
,
146
, p.
106113
.10.1016/j.ijthermalsci.2019.106113
39.
Mulamootil
,
J. K.
,
Rath
,
S.
, and
Dash
,
S. K.
,
2021
, “
Relative Importance of Temperature-Dependent Properties in Non-Newtonian Natural Convection Around Curved Surfaces
,”
Int. Commun. Heat Mass Transfer
,
124
, p.
105263
.10.1016/j.icheatmasstransfer.2021.105263
40.
Rath
,
S.
, and
Dash
,
S. K.
,
2021
, “
Effect of Horizontal Spacing on Natural Convection to Power-Law Fluids From Two Horizontally Aligned Cylinders
,”
Heat Transfer Eng.
,
42
(
10
), pp.
854
874
.10.1080/01457632.2020.1744251
41.
Rath
,
S.
, and
Dash
,
S. K.
,
2021
, “
Natural Convection in Power-Law Fluids From a Pair of Two Attached Horizontal Cylinders
,”
Heat Transfer Eng.
,
42
(
7
), pp.
627
653
.10.1080/01457632.2020.1716487
You do not currently have access to this content.