Heat conduction in a plane wall subject to periodic temperature changes |
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Authors: | Dr J C Hein |
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Institution: | (1) Lurgi Chemie und Hüttentechnik GmbH, Gervinusstr. 17-19, 6000 Frankfurt/Main 11 |
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Abstract: | Analytical solutions for the heat conduction in a plane wall with periodic temperature variations at the wall surface are presented. Series and asymptotic developments of these solutions are deduced. The results are important for the calculation of the heat transfer in rotary kilns or other rotaring units.
Die Wärmeleitung in einer ebenen Wand mit periodischen Temperaturänderungen Zusammenfassung Es werden analytische Lösungen für die Wärmeleitung in einer ebenen Wand mit periodischen Temperaturänderungen an ihrer Oberfläche mitgeteilt. Reihen- und asymptotische Entwicklungen dieser Lösungen werden abgeleitet. Die Ergebnisse sind wichtig für die Berechnung des Wärmetransportes in Drehrohröfen oder ähnlichen Maschinen. Nomenclature
a
2
= / C m2/s
thermal diffusivity, Eq. (1)
-
C J/kg K
specific heat
-
F K
initial temperature of the wall, Eq. (4)
-
F m2
surface of the wall
-
G
Green's function, Eq. (10)
- G1
Green's function, Eq. (12)
-
h m
thickness of the wall
-
H
Heaviside function, Eq. (5)
-
k
constant, Eq. (25)
-
k
x
constant, Eq. (25)
-
Q J
total energy, Eq. (17)
-
Q
u
J
total energy from temperatureU, Eq. (18)
-
Q
v
J
total energy from temperatureV, Eq. (19)
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s s–1
Laplace variable
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t s
time
-
t
1
s
heating time, Eq. (5)
-
t
2
s
period, Eq. (5)
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T K
temperature of the wall
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T
i
K
surface temperature of the wall
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T
1
K
surface temperature of the wall during the heating time
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T
2
K
surface temperature of the wall during the cooling time
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U K
temperature of the wall defined in problem 1
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V, K
temperature of the wall defined in problem 2
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x m
coordinate
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0
W/m2K
overall heat transfer coefficient, Eq. (31)
- 10 W/m2 K
overall heat transfer coefficient, Eq. (32)
- 20 W/m2 K
overall heat transfer coefficient, Eq. (33)
-
Dirac Delta function
- s–1/2
parameter, Eq. (6)
-
W/mK
thermal conductivity
-
kg/m3
specific mass
-
dimensionless time, Eq. (34)
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Riemann Zeta function
surfix
Laplace transformed variable |
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Keywords: | |
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