Abstract
A computational work is performed on laminar free convection from an isothermally heated spherical shaped open cavity with negligible wall thickness suspended in the air. Fluid flow and heat transfer are analyzed in detail by solving governing differential equations (continuity, momentum, and energy) numerically over wide ranges of the relevant dimensionless parameters, namely, Rayleigh number, 104 ≤ Ra ≤ 108; and height to diameter ratio, 0.15 ≤ h/D ≤ 0.95. The detailed behavior of thermal and flow fields is delineated by suitable visualization techniques for different Ra and h/D. The influence of Ra and h/D on the local and average Nusselt number is also predicted and it is observed that the average Nusselt number on both outer and inner surfaces decreases with the increase of h/D for a constant value of Ra. A suitable correlation for the net average Nusselt number is obtained for the spherical-shaped open vessel surface as a function of Ra, and h/D based on the computed data points, which is expected to be relevant for various academic and industrial operations. This study can be helpful in various industrial operations, such as heat treatment of foodstuffs, shield surfaces, thermal insulations, melting of polymer pellets, and fluidized reactors.
Issue Section:
Natural and Mixed Convection
References
1.
Hassan
,
K. E.
, and
Mohamed
,
S. A.
, 1970
, “
Natural Convection From Isothermal Flat Surfaces
,” Int. J. Heat Mass Transfer
,
13
(12
), pp. 1873
–1886
.10.1016/0017-9310(70)90090-62.
Schaub
,
M.
,
Kriegel
,
M.
, and
Brandt
,
S.
, 2019
, “
Analytical Prediction of Heat Transfer by Unsteady Natural Convection at Vertical Flat Plates in Air
,” Int. J. Heat Mass Transfer
,
144
, p. 118665
.10.1016/j.ijheatmasstransfer.2019.1186653.
Roy
,
S.
, and
Anilkumar
,
D.
, 2006
, “
Unsteady Mixed Convection From a Moving Vertical Slender Cylinder
,” ASME J. Heat Transfer-Trans. ASME
,
128
(4
), pp. 368
–373
.10.1115/1.21652064.
Heckel
,
J. J.
,
Chen
,
T. S.
, and
Armaly
,
B. F.
, 1989
, “
Mixed Convection Along Slender Vertical Cylinders With Variable Surface Temperature
,” Int. J. Heat Mass Transfer
,
32
(8
), pp. 1431
–1442
.10.1016/0017-9310(89)90067-75.
Kang
,
G. U.
, and
Yook
,
D. S.
, 2019
, “
Laminar Natural Convection Heat Transfer Depending on Diameters of Vertical Cylinders With Circular Cross-Section With High Prandtl Number
,” Int. J. Heat Mass Transfer
,
134
, pp. 554
–565
.10.1016/j.ijheatmasstransfer.2019.01.0736.
Acharya
,
S.
,
Agrawal
,
S.
, and
Dash
,
S. K.
, 2018
, “
Numerical Analysis of Natural Convection Heat Transfer From a Vertical Hollow Cylinder Suspended in Air
,” ASME J. Heat Transfer-Trans. ASME
,
140
(5
), p. 052501
.10.1115/1.40384787.
Rana
,
B. K.
,
Singh
,
B.
, and
Senapati
,
J. R.
, 2021
, “
Thermofluid Characteristics on Natural and Mixed Convection Heat Transfer From a Vertical Rotating Hollow Cylinder Immersed in Air: A Numerical Exercise
,” ASME J. Heat Transfer-Trans. ASME
,
143
(2
), p. 022601
.10.1115/1.40488308.
Rana
,
B. K.
, and
Senapati
,
J. R.
, 2021
, “
Entropy Generation Analysis and Cooling Time Estimation for a Rotating Vertical Hollow Tube in the Air Medium
,” ASME J. Heat Transfer-Trans. ASME
,
143
(4
), p. 042101
.10.1115/1.40498399.
Rana
,
B. K.
, 2022
, “
Conjugate Steady Natural Convection Analysis Around Thick Tapered Vertical Pipe Suspended in the Air
,” Sādhanā
,
47
(1
), pp. 1
–16
.10.1007/s12046-021-01780-410.
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)00259-611.
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/S002211208000139512.
Singh
,
S. N.
, and
Hasan
,
M. M.
, 1983
, “
Free Convection About a Sphere at Small Grashof Number
,” Int. J. Heat Mass Transfer
,
26
(5
), pp. 781
–783
.10.1016/0017-9310(83)90028-513.
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.2010.09.00314.
Bruneau
,
C. H.
,
Fischer
,
P.
,
Xiong
,
Y. L.
, and
Kellay
,
H.
, Cyclobulle Collaboration
2018
, “
Numerical Simulations of Thermal Convection on a Hemisphere
,” Phys. Rev. Fluids
,
3
(4
), p. 043502
.10.1103/PhysRevFluids.3.04350215.
Liu
,
J.
,
Zhao
,
C. J.
,
Liu
,
H.
, and
Lu
,
W. Q.
, 2018
, “
Numerical Study of Laminar Natural Convection Heat Transfer From a Hemisphere With Adiabatic Plane and Isothermal Hemispherical Surface
,” Int. J. Therm. Sci.
,
131
, pp. 132
–143
.10.1016/j.ijthermalsci.2018.05.01316.
Zhang
,
J.
,
Liu
,
J.
, and
Lu
,
W.
, 2019
, “
Study on Laminar Natural Convection Heat Transfer From a Hemisphere With Uniform Heat Flux Surface
,” J. Therm. Sci.
,
28
(2
), pp. 232
–245
.10.1007/s11630-018-1051-y17.
Behera
,
S.
,
Acharya
,
S.
, and
Dash
,
S. K.
, 2020
, “
Natural Convection Heat Transfer From Linearly, Circularly and Parabolically Bent Plates: A Study of Shape Effect
,” Int. J. Therm. Sci.
,
150
, p. 106219
.10.1016/j.ijthermalsci.2019.10621918.
Nasr
,
K. B.
,
Chouikh
,
R.
,
Kerkeni
,
C.
, and
Guizani
,
A.
, 2006
, “
Numerical Study of the Natural Convection in Cavity Heated From the Lower Corner and Cooled From the Ceiling
,” Appl. Therm. Eng.
,
26
(7
), pp. 772
–775
.10.1016/j.applthermaleng.2005.09.01119.
Johnson
,
C. E.
, 1986
, “
Evaluation of Correlations for Natural Convection Cooling of Electronic Equipment
,” Heat Transfer Eng.
,
7
(1–2
), pp. 36
–45
.10.1080/0145763860893964320.
Yeh
,
L. T.
, 1995
, “
Review of Heat Transfer Technologies in Electronic Equipment
,” ASME J. Electron. Packag
,
117
(4
), pp. 333
–339
.10.1115/1.279211321.
Incropera
,
F. P.
, 1988
, “
Convection Heat Transfer in Electronic Equipment Cooling
,” ASME J. Heat Transfer-Trans. ASME
,
110
(4b
), pp. 1097
–1111
.10.1115/1.325061322.
Baïri
,
A.
,
De María
,
J. G.
,
Baïri
,
I.
,
Laraqi
,
N.
,
Zarco-Pernia
,
E.
, and
Alilat
,
N.
, 2012
, “
2D Transient Natural Convection in Diode Cavities Containing an Electronic Equipment With Discrete Active Bands Under Constant Heat Flux
,” Int. J. Heat Mass Transfer
,
55
(19–20
), pp. 4970
–4980
.10.1016/j.ijheatmasstransfer.2012.04.03223.
Xin
,
R. C.
, and
Ebadian
,
M. A.
, 1996
, “
Natural Convection Heat Transfer From Helicoidal Pipes
,” J. Thermophys. Heat Transfer
,
10
(2
), pp. 297
–302
.10.2514/3.78724.
Garoosi
,
F.
,
Hoseininejad
,
F.
, and
Rashidi
,
M. M.
, 2016
, “
Numerical Study of Natural Convection Heat Transfer in a Heat Exchanger Filled With Nanofluids
,” Energy
,
109
, pp. 664
–678
.10.1016/j.energy.2016.05.05125.
Spitler
,
J. D.
,
Javed
,
S.
, and
Ramstad
,
R. K.
, 2016
, “
Natural Convection in Groundwater-Filled Boreholes Used as Ground Heat Exchangers
,” Appl. Energy
,
164
, pp. 352
–365
.10.1016/j.apenergy.2015.11.04126.
Dimmick
,
G. R.
,
Chatoorgoon
,
V.
,
Khartabil
,
H. F.
, and
Duffey
,
R. B.
, 2002
, “
Natural-Convection Studies for Advanced CANDU Reactor Concepts
,” Nucl. Eng. Des.
,
215
(1–2
), pp. 27
–38
.10.1016/S0029-5493(02)00039-027.
Liu
,
L.
,
Deng
,
J.
,
Zhang
,
D.
,
Wang
,
C.
,
Qiu
,
S.
, and
Su
,
G. H.
, 2020
, “
Experimental Analysis of Flow and Convective Heat Transfer in the Water-Cooled Packed Pebble Bed Nuclear Reactor Core
,” Prog. Nucl. Energy
,
122
, p. 103298
.10.1016/j.pnucene.2020.10329828.
Wu
,
S. Y.
,
Xiao
,
L.
, and
Li
,
Y. R.
, 2011
, “
Effect of Aperture Position and Size on Natural Convection Heat Loss of a Solar Heat-Pipe Receiver
,” Appl. Therm. Eng.
,
31
(14–15
), pp. 2787
–2796
.10.1016/j.applthermaleng.2011.05.00429.
Manzoor
,
M. T.
,
Lenci
,
G.
, and
Tetreault-Friend
,
M.
, 2021
, “
Convection in Volumetrically Absorbing Solar Thermal Receivers: A Theoretical Study
,” Sol. Energy
,
224
, pp. 1358
–1368
.10.1016/j.solener.2021.06.04830.
de Vahl Davis
,
G.
, 1983
, “
Natural Convection of Air in a Square Cavity: A Bench Mark Numerical Solution
,” Int. J. Numer. Methods Fluids
,
3
(3
), pp. 249
–264
.10.1002/fld.165003030531.
Markatos
,
N. C.
, and
Pericleous
,
K. A.
, 1984
, “
Laminar and Turbulent Natural Convection in an Enclosed Cavity
,” Int. J. Heat Mass Transfer
,
27
(5
), pp. 755
–772
.10.1016/0017-9310(84)90145-532.
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)90187-333.
Shiina
,
Y.
,
Fujimura
,
K.
,
Kunugi
,
T.
, and
Akino
,
N.
, 1994
, “
Natural Convection in a Hemispherical Enclosure Heated From Below
,” Int. J. Heat Mass Transfer
,
37
(11
), pp. 1605
–1617
.10.1016/0017-9310(94)90176-734.
Lewandowski
,
W. M.
,
Kubski
,
P.
,
Khubeiz
,
J. M.
,
Bieszk
,
H.
,
Wilczewski
,
T.
, and
Szymański
,
S.
, 1996
, “
Theoretical and Experimental Study of Natural Convection Heat Transfer From Isothermal Hemisphere
,” Int. J. Heat Mass Transfer
,
40
(1
), pp. 101
–109
.10.1016/S0017-9310(96)00075-035.
Khubeiz
,
J. M.
,
Radziemska
,
E.
, and
Lewandowski
,
W. M.
, 2002
, “
Natural Convective Heat-Transfers From an Isothermal Horizontal Hemispherical Cavity
,” Appl. Energy
,
73
(3–4
), pp. 261
–275
.10.1016/S0306-2619(02)00079-X36.
Prakash
,
M.
,
Kedare
,
S. B.
, and
Nayak
,
J. K.
, 2012
, “
Numerical Study of Natural Convection Loss From Open Cavities
,” Int. J. Therm. Sci.
,
51
, pp. 23
–30
.10.1016/j.ijthermalsci.2011.08.01237.
Baïri
,
A.
, and
Öztop
,
H. F.
, 2014
, “
On Thermal Control of Devices Contained in Inclined Hemispherical Cavities With Dome Oriented Downwards and Subjected to Transient Natural Convection
,” Int. Commun. Heat Mass Transfer
,
55
, pp. 109
–112
.10.1016/j.icheatmasstransfer.2014.04.00138.
Baïri
,
A.
, and
de María
,
J. G.
, 2013
, “
Numerical and Experimental Study of Steady State Free Convection Generated by Constant Heat Flux in Tilted Hemispherical Cavities
,” Int. J. Heat Mass Transfer
,
66
, pp. 355
–365
.10.1016/j.ijheatmasstransfer.2013.07.03839.
Baïri
,
A.
,
Monier-Vinard
,
E.
,
Laraqi
,
N.
,
Baïri
,
I.
,
Nguyen
,
M. N.
, and
Dia
,
C. T.
, 2014
, “
Natural Convection in Inclined Hemispherical Cavities With Isothermal Disk and Dome Faced Downwards. Experimental and Numerical Study
,” Appl. Therm. Eng.
,
73
(1
), pp. 1340
–1347
.10.1016/j.applthermaleng.2014.09.01240.
Baïri
,
A.
, 2014
, “
Quantification of Natural Convective Heat Transfer Within Air-Filled Hemispherical Cavities. Isothermal Tilted Disk With Dome Oriented Upwards and Wide Ra Range
,” Int. Commun. Heat Mass Transfer
,
57
, pp. 291
–296
.10.1016/j.icheatmasstransfer.2014.07.00941.
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.2014.10.02842.
Zhang
,
J.
,
Zhen
,
Q.
,
Liu
,
J.
, and
Lu
,
W. Q.
, 2019
, “
Effect of Spacing on Laminar Natural Convection Flow and Heat Transfer From Two Spheres in Vertical Arrangement
,” Int. J. Heat Mass Transfer
,
134
, pp. 852
–865
.10.1016/j.ijheatmasstransfer.2019.01.06543.
Lee
,
D.
,
Jang
,
H.
,
Lee
,
B. J.
,
Choi
,
W.
, and
Byon
,
C.
, 2019
, “
Internal Natural Convection Around a Sphere in a Rectangular Chamber
,” Int. J. Heat Mass Transfer
,
136
, pp. 501
–509
.10.1016/j.ijheatmasstransfer.2019.03.02344.
Nazeer
,
M.
,
Ali
,
N.
,
Javed
,
T.
, and
Asghar
,
Z.
, 2018
, “
Natural Convection Through Spherical Particles of a Micropolar Fluid Enclosed in a Trapezoidal Porous Container
,” Eur. Phys. J. Plus
,
133
(10
), p. 423
.10.1140/epjp/i2018-12217-545.
Nazeer
,
M.
,
Ali
,
N.
, and
Javed
,
T.
, 2018
, “
Numerical Simulation of MHD Flow of Micropolar Fluid Inside a Porous Inclined Cavity With Uniform and Non-Uniform Heated Bottom Wall
,” Can. J. Phys.
,
96
(6
), pp. 576
–593
.10.1139/cjp-2017-063946.
Nazeer
,
M.
,
Ali
,
N.
, and
Javed
,
T.
, 2018
, “
Natural Convection Flow of Micropolar Fluid Inside a Porous Square Conduit: Effects of Magnetic Field, Heat Generation/Absorption, and Thermal Radiation
,” J. Porous Media
,
21
(10
), pp. 953
–975
.10.1615/JPorMedia.201802112347.
Ali
,
N.
,
Nazeer
,
M.
,
Javed
,
T.
, and
Siddiqui
,
M. A.
, 2018
, “
Buoyancy-Driven Cavity Flow of a Micropolar Fluid With Variably Heated Bottom Wall
,” Heat Transfer Res.
,
49
(5
), pp. 457
–481
.10.1615/HeatTransRes.201801942248.
Nazeer
,
M.
,
Ali
,
N.
,
Javed
,
T.
, and
Razzaq
,
M.
, 2019
, “
Finite Element Simulations for Energy Transfer in a Lid-Driven Porous Square Container Filled With Micropolar Fluid: Impact of Thermal Boundary Conditions and Peclet Number
,” Int. J. Hydrogen Energy
,
44
(14
), pp. 7656
–7666
.10.1016/j.ijhydene.2019.01.23649.
Nazeer
,
M.
,
Ali
,
N.
, and
Javed
,
T.
, 2019
, “
Numerical Simulations of MHD Forced Convection Flow of Micropolar Fluid Inside a Right-Angled Triangular Cavity Saturated With Porous Medium: Effects of Vertical Moving Wall
,” Can. J. Phys.
,
97
(1
), pp. 1
–13
.10.1139/cjp-2017-090450.
Nazir
,
M. W.
,
Javed
,
T.
,
Ali
,
N.
, and
Nazeer
,
M.
, 2021
, “
Effects of Radiative Heat Flux and Heat Generation on Magnetohydodynamics Natural Convection Flow of Nanofluid Inside a Porous Triangular Cavity With Thermal Boundary Conditions
,” Numer. Methods Partial Differ. Equ.
, pp. 1
–18
.10.1002/num.2276851.
Ali
,
N.
,
Nazeer
,
M.
, and
Javed
,
T.
, 2021
, “
Finite Element Simulations of Free Convection Flow Inside a Porous Inclined Cavity Filled With Micropolar Fluid
,” J. Porous Media
,
24
(2
), pp. 57
–75
.10.1615/JPorMedia.202002497752.
Saxena
,
A.
,
Kishor
,
V.
,
Singh
,
S.
, and
Srivastava
,
A.
, 2018
, “
Experimental and Numerical Study on the Onset of Natural Convection in a Cavity Open at the Top
,” Phys. Fluids
,
30
(5
), p. 057102
.10.1063/1.502509253.
Saxena
,
A.
,
Singh
,
S.
, and
Srivastava
,
A.
, 2018
, “
Flow and Heat Transfer Characteristics of an Open Cubic Cavity With Different Inclinations
,” Phys. Fluids
,
30
(8
), p. 087101
.10.1063/1.504069854.
Behera
,
B. R.
,
Chandrakar
,
V.
, and
Senapati
,
J. R.
, 2021
, “
Free Convection Heat Transfer From a Concave Hemispherical Surface: A Numerical Exercise
,” Int. Commun. Heat Mass Transfer
,
125
, p. 105324
.10.1016/j.icheatmasstransfer.2021.10532455.
Kishor
,
V.
,
Singh
,
S.
, and
Srivastava
,
A.
, 2021
, “
Flow Instabilities and Heat Transfer in a Differentially Heated Cavity Placed at Varying Inclination Angles: Non-Intrusive Measurements
,” Phys. Fluids
,
33
(9
), p. 094103
.10.1063/5.0063217Copyright © 2022 by ASME
You do not currently have access to this content.
