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Chapter 2
Heat Conduction Equation
216
The rate of heat generation per unit volume in the uranium rods is given. The total rate of heat
generation in each rod is to be determined.
Assumptions
Heat is generated uniformly in the uranium rods.
g
= 7
×
10
7
W/m
3
L
= 1 m
D
= 5 cm
Analysis
The total rate of heat generation in the rod is
determined by multiplying the rate of heat generation per unit
volume by the volume of the rod
&
&&
(/
)
(
)
(
.
/
]
(
Gg
V
gD
L
==
=
×
=×
rod
32
5
W / m [
m)
m)
1.374 10 W =
ππ
27
47
1
0
0
0
54
1
137.4 kW
217
The variation of the absorption of solar energy in a solar pond with depth is given. A relation for the
total rate of heat generation in a water layer at the top of the pond
is to be determined.
Assumptions
Absorption of solar radiation by water is modeled as heat generation.
Analysis
The total rate of heat generation in a water layer of surface area
A
and thickness
L
at the top of the
pond
is determined by integration to be
b
)
e
(1
g
A
bL
0
−
−
=
−
−
=
−
=
=
=
∫
∫
&
&
&
&
&
L
bx
L
x
bx
V
b
e
g
A
Adx
e
g
dV
g
G
0
0
0
0
)
(
218
The rate of heat generation per unit volume in a stainless steel plate is given. The heat flux on the
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat

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