Abstract

The influence of non-uniform heating conditions on the buoyancy-driven flow established in an open square cavity with ventilation ports is studied. Cavity configuration is shaped to electronic device with passive cooling. Numerical results for relevant parameters are presented as a function of the Rayleigh number, considering both fixed temperature and heat flux heating conditions. The results obtained retaining the temperature-dependent thermophysical properties are compared with those calculated under the Boussinesq approximation. The impact that the non-uniformly heated wall produces on the thermal and dynamic behavior of the airflow is analyzed. The choice of a given heating distribution slope can produce a thermal behavior improvement, even increasing heat transfer above 20%. Some practical engineering correlations are presented. In fact, a correlation for the critical heating parameter for isoflux heating condition, concerned to the burnout phenomenon, is obtained from numerical results. The effects of the non-uniform heating condition (heat flux case) are not too relevant on this particular phenomenon.

References

References
1.
W
,
E.
,
1942
, “
Heat Dissipation of Parallel Plates by Free Convection
,”
Physica
.,
9
(
1
), pp.
1
28
. 10.1016/S0031-8914(42)90053-3
2.
Incropera
,
F. P.
, and
de Witt
,
D. P.
,
1990
,
Introduction to Heat Transfer
,
Wiley and Sons
,
New York
.
3.
Bejan
,
A.
,
1993
,
Heat Transfer
,
Wiley
,
New York
.
4.
Ostrach
,
S.
,
1972
, “
Natural Convection in Enclosures
,”
Adv. Heat Transf.
,
8
, pp.
161
227
. 10.1016/S0065-2717(08)70039-X
5.
Henkes
,
R. A. W. M.
, and
Hoogendorn
,
C. J.
,
1995
, “
Comparison Exercise for Computations of Turbulent Natural Convection in Enclosures
,”
Numer. Heat Transfer, Part B
,
28
(
1
), pp.
1879
1891
. 10.1080/10407799508928821
6.
Versteegh
,
T. A.
, and
Nieuwstadt
,
F. T.
,
1999
, “
A Direct Numerical Simulation of Natural Convection Between Two Infinite Vertical Differentially Heated Walls Scaling Laws and Wall Functions
,”
Int. J. Heat Mass Transfer
,
42
(
19
), pp.
3673
3693
. 10.1016/S0017-9310(99)00037-X
7.
Chenoweth
,
D. R.
, and
Paolucci
,
S.
,
1986
, “
Natural Convection in an Enclosed Vertical Air Layer With Large Horizontal Temperature Differences
,”
J. Fluid Mechanics
,
169
, pp.
173
210
. 10.1017/S0022112086000587
8.
Emery
,
A. F.
, and
Lee
,
J. W.
,
1999
, “
The Effects of Property Variations on Natural Convection in a Square Enclosure
,”
ASME J. Heat Transfer
,
121
(
1
), pp.
57
62
. 10.1115/1.2825966
9.
Desrayaud
,
G.
,
Chénier
,
E.
,
Joulin
,
A.
,
Bastide
,
A.
,
Brangeon
,
B.
,
Caltagirone
,
J. P.
,
Cherif
,
Y.
,
Eymard
,
R.
,
Garnier
,
C.
,
Giroux-Julien
,
S.
,
Harnane
,
Y.
,
Joubert
,
P.
,
Laaroussi
,
N.
,
Lassue
,
S.
,
Le Quéré
,
P.
,
Li
,
R.
,
Saury
,
D.
,
Sergent
,
A.
,
Xin
,
S.
, and
Zoubir
,
A.
,
2013
, “
Benchmark Solutions for Natural Convection Flows in Vertical Channels Submitted to Different Open Boundary Conditions
,”
Int. J. Therm. Sci.
,
72
, pp.
18
33
. 10.1016/j.ijthermalsci.2013.05.003
10.
Ying
,
X.
,
Ye
,
F.
,
Liu
,
R.
, and
Bao
,
H.
,
2018
, “
Design and Optimization of Thermoelectric Cooling System Under Natural Convection Condition
,”
J. Thermal Sci. Eng. Appl.
,
10
(
5
), p.
051008
. 10.1115/1.4039926
11.
Turan
,
O.
,
Poole
,
R. J.
, and
Chakraborty
,
N.
,
2012
, “
Influences of Boundary Conditions on Laminar Natural Convection in Rectangular Enclosures With Differentially Heated Side Walls
,”
Int. J. Heat Fluid Flow
,
33
(
1
), pp.
131
146
. 10.1016/j.ijheatfluidflow.2011.10.009
12.
Ben Yedder
,
R.
, and
Bilgen
,
E.
,
1995
, “
Turbulent Natural Convection and Conduction in Enclosures Bounded by a Massive Wall
,”
Int. J. Heat Mass Transfer
,
38
(
10
), pp.
1879
1891
. 10.1016/0017-9310(94)00298-A
13.
de Vahl Davies
,
G.
,
1983
, “
Natural Convection of air in a Square Cavity: A Bench Mark Numerical Solution
,”
Int. J. Num. Meth. Fluids
,
3
(
3
), pp.
249
264
. 10.1002/fld.1650030305
14.
Ridouane
,
E. H.
,
Campo
,
A.
, and
Hasnaoui
,
M.
,
2006
, “
Turbulent Natural Convection in an Air-Filled Isosceles Triangular Enclosure
,”
Int. J. Heat Fluid Flow
,
27
(
3
), pp.
476
489
. 10.1016/j.ijheatfluidflow.2005.10.013
15.
Ampofo
,
F.
, and
Karayiannis
,
T. G.
,
2003
, “
Experimental Benchmark Data for Turbulent Natural Convection in an Air Filled Square Cavity
,”
Int. J. Heat Mass Transfer
,
46
(
19
), pp.
3551
3572
. 10.1016/S0017-9310(03)00147-9
16.
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)90145-5
17.
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
. 10.1016/S0017-9310(03)00156-X
18.
Aberuee
,
M. J.
,
Ziaei-Rad
,
M.
, and
Ahmadikia
,
H.
,
2018
, “
The Effects of an Internal Isolated Plate on Natural Convective Heat Transfer Inside an Industrial Oven
,”
Appl. Therm. Eng.
,
144
, pp.
769
778
. 10.1016/j.applthermaleng.2018.08.087
19.
Saha
,
S. K.
,
2019
, “
Numerical Study of Laminar Natural Convection Heat Transfer in Inclined Trapezoidal Enclosure
,”
J. Thermal Sci. Eng. Appl.
,
11
(
6
), p.
061021
. 10.1115/1.4043742
20.
la Pica
,
A.
,
Rodonò
,
G.
, and
Volpes
,
R.
,
1993
, “
An Experimental Investigation on Natural Convection of Air in a Vertical Channel
,”
Int. J. Heat Mass Transfer
,
36
(
3
), pp.
611
616
. 10.1016/0017-9310(93)80036-T
21.
Warrington
,
R. O.
, and
Ameel
,
T. A.
,
1995
, “
Experimental Studies of Natural Convection in Partitioned Enclosures With a Trombe Wall Geometry
,”
J. Solar Energy Eng.
,
117
(
1
), pp.
16
21
. 10.1115/1.2847709
22.
Radhakrishnan
,
T. A.
,
Balaji
,
C.
, and
Venkateshan
,
S. P.
,
2010
, “
Optimization of Multiple Heaters in a Vented Enclosure—A Combined Numerical and Experimental Study
,”
Int. J. Thermal Sci.
,
49
(
4
), pp.
721
732
. 10.1016/j.ijthermalsci.2009.09.012
23.
Moffat
,
R. J.
, and
Anderson
,
A. M.
,
1990
, “
Applying Heat Transfer Coefficient Data to Electronics Cooling
,”
ASME J. Heat Transfer
,
112
(
4
), pp.
882
890
. 10.1115/1.2910495
24.
Wang
,
H. Y.
,
Penot
,
F.
, and
Sauliner
,
J. B.
,
1997
, “
Numerical Study of a Buoyancy-Induced Flow Along a Vertical Plate With Discretely Heated Integrated Circuit Packages
,”
Int. J. Heat Mass Transfer
,
40
(
7
), pp.
1509
1529
. 10.1016/S0017-9310(96)00231-1
25.
da Silva
,
A. K.
,
Lorente
,
S.
, and
Bejan
,
A.
,
2004
, “
Optimal Distribution of Discrete Heat Sources on a Wall With Natural Convection
,”
Int. J. Heat Mass Transfer
,
47
(
2
), pp.
203
214
. 10.1016/j.ijheatmasstransfer.2003.07.007
26.
Bilgen
,
E.
, and
Muftuoglu
,
A.
,
2008
, “
Cooling Strategy by Mixed Convection of a Discrete Heater at Its Optimum Position in a Square Cavity With Ventilation Ports
,”
Int. Comm. Heat Mass Transfer
,
35
(
5
), pp.
545
550
. 10.1016/j.icheatmasstransfer.2008.01.001
27.
Bilgen
,
E.
, and
Balkaya
,
A.
,
2008
, “
Natural Convection on Discrete Heaters in a Square Enclosure With Ventilation Ports
,”
Int. J. Heat Fluid Flow
,
29
(
4
), pp.
1182
1189
. 10.1016/j.ijheatfluidflow.2008.01.013
28.
Hernández
,
J.
, and
Zamora
,
B.
,
2005
, “
Effects of Variable Properties and Non-uniform Heating on Natural Convection Flows in Vertical Channel
,”
Int. J. Heat Mass Transfer
,
48
(
3–4
), pp.
793
807
. 10.1016/j.ijheatmasstransfer.2004.09.024
29.
Roy
,
S.
, and
Basak
,
T.
,
2005
, “
Finite Element Analysis of Natural Convection Flows in a Square Cavity With non-Uniformly Heated Wall(s)
,”
Int. J. Engng. Sci.
,
43
(
8–9
), pp.
668
680
. 10.1016/j.ijengsci.2005.01.002.
30.
Natarajan
,
E.
,
Basak
,
T.
, and
Roy
,
S.
,
2008
, “
Natural Convection Flows in a Trapezoidal Enclosure With Uniform and Non-uniform Heating of Bottom Wall
,”
Int. J. Heat Mass Transfer
,
51
(
3–4
), pp.
747
756
. 10.1016/j.ijheatmasstransfer.2007.04.027
31.
Basak
,
T.
,
Roy
,
S.
,
Babu
,
S. K.
, and
Balakrishnan
,
A. R.
,
2008
, “
Finite Element Analysis of Natural Convection Flow in a Isosceles Triangular Enclosure due to Uniform and non-Uniform Heating at the Side Walls
,”
Int. J. Heat Mass Transfer
,
51
(
17–18
), pp.
4496
4505
. 10.1016/j.ijheatmasstransfer.2007.12.018
32.
Basak
,
T.
,
Roy
,
S.
,
Singh
,
A.
, and
Pop
,
I.
,
2009
, “
Finite Element Simulation of Natural Convection Flow in a Trapezoidal Enclosure Filled With Porous Medium due to Uniform and non-Uniform Heating
,”
Int. J. Heat Mass Transfer
,
52
(
1–2
), pp.
70
78
. 10.1016/j.ijheatmasstransfer.2008.03.032
33.
Saha
,
S. C.
, and
Gu
,
Y. T.
,
2015
, “
Natural Convection in a Triangular Enclosure Heated From Below and non-Uniformly Cooled From Top
,”
ASME J. Heat Transfer
,
80
, pp.
529
538
. 10.1016/j.ijheatmasstransfer.2014.09.047
34.
Saravanan
,
S.
, and
Sivaraj
,
C.
,
2015
, “
Combined Natural Convection and Thermal Radiation in a Square Cavity With a Nonuniformly Heate Plate
,”
Comp. Fluids
,
117
, pp.
125
138
. 10.1016/j.compfluid.2015.05.005
35.
Tkachenko
,
O. A.
,
Timchenko
,
V.
,
Giroux-Julien
,
S.
,
Ménézo
,
C.
,
Yeoh
,
G. H.
,
Reizes
,
J. A.
,
Sanvicente
,
E.
, and
Fossa
,
M.
,
2016
, “
Numerical and Experimental Investigation of Unsteady Natural Convection in a Non-uniformly Heated Vertical Open-Ended Channel
,”
Int. J. Thermal Sci.
,
99
, pp.
9
25
. 10.1016/j.ijthermalsci.2015.07.029
36.
Alshehri
,
S. M.
,
Said
,
I. A.
, and
Usman
,
S.
,
2020
, “
Effect of Nonuniform Isoflux Heating on Natural Convection Heat Transfer in a Prismatic Modular Reactor
,”
Appl. Thermal Eng.
,
176
, p.
115369
, in press.10.1016/j.applthermaleng.2020.115369
37.
Chakkingal
,
M.
,
Kenjeres
,
S.
,
Dadavi
,
I.
,
Tummers
,
M. J.
, and
Kleijn
,
C. R.
,
2020
, “
Numerical Analysis of Natural Convection in a Differentially Heated Packed Bed With Non-uniform Wall Temperature
,”
Int. J. Heat Mass Transfer
,
149
, p.
119168
, in press.10.1016/j.ijheatmasstransfer.2019.119168
38.
Gray
,
D. D.
, and
Giorgini
,
A.
,
1976
, “
The Validity of the Boussinesq Approximation for Liquids and Gases
,”
Int. J. Heat Mass Transfer
,
19
(
5
), pp.
545
551
. 10.1016/0017-9310(76)90168-X
39.
Roy
,
K.
,
Giri
,
A.
, and
Das
,
B.
,
2019
, “
A Computational Study on Natural Convection Heat Transfer From an Inclined Plate Finned Channel
,”
Appl. Therm. Eng.
,
159
, p.
11391
. 10.1016/j.applthermaleng.2019.113941
40.
Guo
,
Z. Y.
, and
Wu
,
X. B.
,
1993
, “
Thermal Drag and Critical Heat Flux for Natural Convection of Air in Vertical Parallel Plates
,”
ASME J. Heat Transfer
,
115
(
1
), pp.
124
129
. 10.1115/1.2910637
41.
Wang
,
L.
,
Huang
,
C.
,
Yang
,
X.
,
Chai
,
Z.
, and
Shi
,
B.
,
2019
, “
Effects of Temperature-Dependent Properties on Natural Convection of Power-Law Nanofluids in Rectangular Cavities With Sinusoidal Temperature Distribution
,”
Int. J. Heat Mass Transfer
,
128
, pp.
688
699
. 10.1016/j.ijheatmasstransfer.2018.09.007
42.
Zamora
,
B.
, and
Kaiser
,
A. S.
,
2012
, “
Influence of the Variable Thermophysical Properties on the Turbulent Buoyancy-Driven Airflow Inside Open Square Cavities
,”
Heat Mass Transfer
,
48
(
1
), pp.
35
53
. 10.1007/s00231-011-0838-0
43.
Çengel
,
Y. A.
, and
Cimbala
,
J. M.
,
2006
,
Fluid Mechanics: Fundamentals and Applications
,
McGraw-Hill
,
New York
.
44.
Kolmogorov
,
A. N.
,
1942
, “
Equations of Turbulent Motion of an Incompressible Fluid
,”
Izvestya Academii Nauk USSR. Phys.
,
6
, pp.
56
58
.
45.
Wilcox
,
D. C.
,
2008
, “
Formulation of the k−ω Turbulence Model Revisited
,”
AIAA J.
,
46
(
11
), pp.
2823
2838
. 10.2514/1.36541
46.
Zamora
,
B.
, and
Kaiser
,
A. S.
,
2016
, “
Radiative Effects on Turbulent Buoyancy-Driven Airflow in Open Square Cavities
,”
Int. J. Thermal Sci.
,
100
, pp.
267
283
. 10.1016/j.ijthermalsci.2015.10.002
47.
Zamora
,
B.
, and
Hernández
,
J.
,
2001
, “
Influence of Upstream Conduction on the Thermally Optimum Spacing of Isothermal, Natural Convection-Cooled Vertical Plate Arrays
,”
Int. Comm. Heat Mass Transfer
,
28
(
2
), pp.
201
210
. 10.1016/S0735-1933(01)00227-5
48.
Wan
,
D. C.
,
Patnaik
,
B. S. V.
, and
Wei
,
G. W.
,
2001
, “
A New Benchmark Quality Solution for the Buoyancy Driven Cavity by Discrete Singular Convolution
,”
Numer. Heat Transfer, Part B
,
40
(
3
), pp.
199
228
. 10.1080/104077901752379620
You do not currently have access to this content.