Chapter 4
Transient Heat Conduction
4111
The trunks of some dry oak trees are exposed to hot gases. The time for the ignition of the trunks is
to be determined.
Assumptions
1
Heat conduction in the trunks is onedimensional since it is long and it has thermal
symmetry about the center line.
2
The thermal properties of the trunks are constant.
3
The heat transfer
coefficient is constant and uniform over the entire surface.
4
The Fourier number is
τ
> 0.2 so that the one
term approximate solutions (or the transient temperature charts) are applicable (this assumption will be
verified).
Properties
The properties of the trunks are given to be
k
= 0.17 W/m.
°
C and
α
= 1.28
×
10
7
m
2
/s.
Analysis
We treat the trunks of the trees as an infinite cylinder since heat transfer is primarily in the radial
direction. Then the Biot number becomes
24
.
38
)
C
W/m.
17
.
0
(
)
m
1
.
0
)(
C
.
W/m
65
(
2
=
°
°
=
=
k
hr
Bi
o
The constants
λ
1
and
A
1
corresponding to this Biot
number are, from Table 41,
5989
.
1
and
3420
.
2
1
1
=
=
A
The Fourier number is
184
.
0
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat, Heat Transfer, TI, Thermal conductivity, transient heat conduction

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