of 22
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Unsteady state Conduction
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dtdTVcTThAs )(
TT
dt
d
hA
Vc
s t
s
dtd
hA
Vc
i 0
TTii thA
Vc i
s
ln
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tVc
hA
TT
TT s
ii
exp
tt
s
t CRVc
hA
)(
1
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The Biot number provides a
measure of the temperature
drop in the solid relative to
the temperature difference
between surface and the fluid
If Bi
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Bik
hL
R
R
hA
kAL
TT
TT
conv
cond
s
ss
)/1(
)/(
2,
2,1,
22
c
c
c
c
c
s
L
t
k
hL
L
t
c
k
k
hL
cL
ht
Vc
thA
FoBiVc
thAs .
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Hyperbolic heat conduction(Non Fourier Heat Conduction)
aC
t
qTq
)()(2
2
Tt
T
t
Tcp
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)exp(),0(.1 0 titx
0),(.2 tx
2
2
2
2
t
t
x
a
Condition :
))1)((2
cos())1)((2
exp(),(22
0
a
xta
xtx
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)2
exp(0
a
xB
12a
xG
1
2)ln(2
22
G
x
B
xa
2
11 2
G
B)ln(
Amplitude ratio
Thermal diffusivity Relaxation time
Phase shift
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Das schematische Schaltbild desMessaufbaues
4. DC Power
Supply
1. Test Cell
Thermocouple
leads
3. Thermostatic Bath
5. Amplifier & Filter
7. PC
6. Data Acquisition
System
2. Cooling Water
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Properties of materials examined
Material
Diameter
particle
Bulk
densitykg/m3
Porosity
copper coated lead
spheres
4.4 - 4.5
mm6300 0,442
synthetic sand (SiO2
) 1670 0.372
Al2O3 (gamma) 6.5 mm 840 0,789
Al2O3 (gamma) 134 nm
NHCO3 1230 0,430
Processed meat
(Bologna)- - -
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Temperature distribution in media
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Comparison of measured values of thermal diffusivity (a) and relaxation time ()
Material Thermal
Diffusivity
[10-6 m2/s]
Relaxation Time
[s]
Source
Sand 0.226
0.408
0.2180.169
2.26
20
00
Present experiment
Kaminski 1990
Gramann et al. 1999Herwig et al. 2000
NaHCO3 0.185
0.31
0.66
28.7
Present experiment
Kaminski 1990
ProcessedMeat
0.1320.14
0.1304
1.7715.5
0
Present experimentMitra et al. 1995
Herwig et al. 2000
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Thermal diffusivity and Relaxation time ofPb-Cu with He, N2 and Ar as filling gases
0
1
2
3
0 0.5 1 1.5 2 2.5
Druck [bar]
Temperaturleitfhigkeit[10-6m2/s]
Pb-Cu mit N2
Pb-Cu mit He
Pb-Cu mit Ar
10
12
14
16
18
20
22
24
0 0.5 1 1.5 2 2.5
Druck [bar]
RelaxationZeit[s] Pb-Cu mit N2
Pb-Cu mit He
Pb-Cu mit Ar
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Temperature effect
Pb-Cu (mit Gas Helium)
0
0.5
1
1.5
2
2.5
3
0 0.5 1 1.5 2 2.5
Druck [bar]
Tem
peraturleitfhigkeit[1
0-6m
2/s]
Temp (27.5C)
Temp (32.5C)
Temp (40C)
Pb-Cu (mitGas Helium)
0
5
10
15
20
25
0 0.5 1 1.5 2 2.5
Druck [bar]
Relaxationzeit[s]
Temp (27.5C)
Temp (32.5C)
Temp (40C)
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Effekt der Partikelgre
0
0.05
0.1
0.15
0.2
0.25
0.3
0 0.5 1 1.5 2 2.5
Druck [bar]
Teperaturlitfhigkeit
[10-6m
2/s]
Al2O3 (in nm)
Al2O3 (in mm)
0
5
10
15
20
25
30
35
40
45
50
0 0.5 1 1.5 2 2.5
Druck [bar]
Relaxationzeit[s]
Al2O3 (in nm)
Al2O3 (in mm)
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The second wave velocity
0
0,05
0,1
0,15
0,2
0,25
0 0,5 1 1,5 2 2,5
Pressure [bar]
SecondSoundWaveV
elocity[mm/s]
Temp 15 C
Temp 20 C
Temp 25 C
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 0.5 1 1.5 2 2.5
Druck [bar]
ZweiteSchallgeschwindigkeit[mm/s]
Al2O3 (in nm)
Al2O3 (in mm)
