PROBLEM 4.9
K
NOWN:
Heat generation in a buried spherical container.
FIND:
(a) Outer surface temperature of the container, (b) Representative isotherms and heat
low lines.
f
SCHEMATIC:
ASSUMPTIONS:
(1) Steadystate conditions, (2) Soil is a homogeneous medium with
onstant properties.
c
P
ROPERTIES:
Table A3
, Soil (300K): k = 0.52 W/m
⋅
K.
ANALYSIS:
(a) From an energy balance on the container,
and from the first entry in
able 4.1,
g
qE
=
±
T
()
12
2D
qk
T
lD
/
4
z
T
.
π
=−
−
H
ence,
q 1 D/4z
500W
1 2m/40m
T
T
20 C+
92.7 C
W
k2D
2 2
m
0.52
mK
ππ
−−
=+
=
=
⋅
DD
<
(b) The isotherms may be viewed as spherical surfaces whose center moves downward with
increasing radius.
The surface of the soil is an isotherm for which the center is at z =
∞
.
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View Full DocumentPROBLEM 4.10
K
NOWN:
Temperature, diameter and burial depth of an insulated pipe.
F
IND:
Heat loss per unit length of pipe.
SCHEMATIC:
ASSUMPTIONS:
(1) Steadystate conditions, (2) Onedimensional conduction through
insulation, twodimensional through soil, (3) Constant properties, (4) Negligible oil
onvection and pipe wall conduction resistances.
c
PROPERTIES:
Table A3
, Soil (300K):
k = 0.52 W/m
⋅
K;
Table A3
, Cellular glass (365K):
= 0.069 W/m
⋅
K.
k
A
NALYSIS:
The heat rate can be expressed as
12
tot
TT
q
R
−
=
w
here the thermal resistance is R
tot
= R
ins
+ R
soil
.
From Equation 3.28,
()
( )
21
ins
ins
n D / D
n 0.7m/0.5m
0.776m K/W
R.
2 Lk
2 L 0.069 W/m K
L
ππ
⋅
==
=
×⋅
AA
F
rom Equation 4.21 and Table 4.1,
1
1
2
soil
soil
soil
cosh
2z/D
cosh
3/ 0.7
1
0.653
Rm
Sk
2
0.52 W/m K L
L
=
=
⋅
K
/
W
.
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 Spring '11
 Anthony
 Heat, Heat Transfer, heat sink, heat loss, thermal resistance, 30pin fin heat

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