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Chapter 3
Steady Heat Conduction
338E
A thin copper plate is sandwiched between two layers of epoxy boards. The effective thermal
conductivity of the board along its 9 in long side and the fraction of the heat conducted through copper
along that side are to be determined.
Assumptions
1
Steady operating conditions exist.
2
Heat transfer is onedimensional since heat transfer
from the side surfaces are disregarded
3
Thermal conductivities are constant.
Properties
The thermal conductivities are given to be
k
= 223 Btu/h
⋅
ft
⋅
°F for copper and 0.15 Btu/h
⋅
ft
⋅
°F
for epoxy layers.
Analysis
We take the length in the direction of heat transfer to be
L
and the width of the board to be
w
.
Then heat conduction along this twolayer plate can be expressed as (we treat the two layers of epoxy as a
single layer that is twice as thick)
[]
L
T
w
kt
kt
L
T
kA
L
T
kA
Q
Q
Q
Δ
+
=
⎟
⎠
⎞
⎜
⎝
⎛
Δ
+
⎟
⎠
⎞
⎜
⎝
⎛
Δ
=
+
=
epoxy
copper
epoxy
copper
epoxy
copper
)
(
)
(
&
&
&
Heat conduction along an “equivalent” plate of thick ness
t
=
t
copper
+
t
epoxy
and thermal conductivity
k
eff
can be expressed as
L
T
w
t
t
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Conductivity, Mass, Heat

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