numerical solution for the radiative heat distribution in a cylindrical enclosure cosmin dan,...
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NUMERICAL SOLUTION FOR THE RADIATIVE HEAT
DISTRIBUTION IN A CYLINDRICAL ENCLOSURE
Cosmin Dan, Gilbert De Mey, Erik Dick
University of Ghent, Belgium
MIXDES 2003 2
Overview
• Introduction• The net radiation method• The configuration factors
computation• Results• Conclusions
MIXDES 2003 3
Introduction
• Motivation
Electronic Package
Heat source
Reflected heat
Incident heat Transmitted heat
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Introduction
ZPk
Transmission line – Wave guide
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Introduction
• Assumptions:– Cylindrical enclosure made of aluminium– Very well polished surfaces– Known temperature distribution – Known emissivity of the inner walls– The surfaces are diffuse gray– The cylinder is divided in small finite
areas (ring shape)
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• The cavity is divided in small areas in which:– The surfaces are isothermal– The surfaces are diffuse emitters and reflectors– The surfaces are gray
The net radiation method
qk
qik
q0k
Sk
ikkk qqq 0
ikkkkk qTq 10
N
jjkjik qFq
10
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• Two energy balance equations
The net radiation method
)(1 0
4kk
k
kk qTq
N
jjkjkk qFqq
100
)()(1
1
44
1
4
1
N
jjkkj
N
jkjkjjj
N
j j
jkj
j
kj TTFFTqF
kjkj CqA
-Gaussian elimination-configuration factors
computation
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R
L
Twall, εwall
Surface i
Tsource, εsource
Tambient
The net radiation method
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The configuration factors
2
1
2221 4
21
RR
XXF
A1
A2
r2
r1
h
R
x
Ai1 Ai2 Aj1 Aj2
Ai
Aj
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The configuration factors
)()(11222211211 ijijjijijj
iji FFAFFA
AF
)()(1
1
44
1
4
1
N
jjkkj
N
jkjkjjj
N
j j
jkj
j
kj TTFFTqF
j
jkj
j
kjkj Fa
1
N
jjkkjk TTFc
1
44 )(
MIXDES 2003 11
Results
0
2
4
6
8
10
12
14
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Cylinder length [m]
q/qi
[-]
q/qi-analytical
q/qi-numerical
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Results
00.5
11.5
22.5
33.5
44.5
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Cylinder length [m]
Rel
ativ
e er
ror
[%]
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Results
00.5
11.5
22.5
33.5
44.5
5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Cylinder length [m]
Rel
ativ
e er
ror
[%]
MIXDES 2003 14
Results
0.00E+00
5.00E+01
1.00E+02
1.50E+02
2.00E+02
2.50E+02
3.00E+02
3.50E+02
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Cylinder length [m]
Hea
t Flo
w [W
/m^2
]
N=20N=100N=200
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Results
0
10
20
30
40
50
60
70
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Cylinder length [m]
Hea
t Flo
w [W
/m^2
]
emissivity 0.1emissivity 0.5emissivity 0.9
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Results
-350
-300
-250
-200
-150
-100
-50
00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cylinder length [m]
Rad
iativ
e flu
x [W
/m^2
]
emissivity 0.1emissivity 0.5emissivity 0.9
MIXDES 2003 17
Results
-250
-200
-150
-100
-50
0
50
100
150
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Cylinder length [m]
Rad
iativ
e flu
x [W
/m^2
]
0.10.50.9
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Conclusions
• A software was developed in order to calculate the heat flow distribution along cylinder wall was realised
• The results obtained using the numerical solution were validated against an analytical case from the literature (R. Siegel, J. R. Howell, “Thermal Radiation Heat Transfer”, 1992, pp. 428-430, pp. 464-467, pp. 477)
• In the future work the obtained results are to be used together with experimental data
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Thank You
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