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Chapter 4
Transient Heat Conduction
475
A semiinfinite aluminum cylinder is cooled by water. The temperature at the center of the cylinder 10
cm from the end surface is to be determined.
Assumptions
1
Heat conduction in the semiinfinite cylinder is twodimensional, and thus the temperature
varies in both the axial
x
 and the radial
r
 directions.
2
The thermal properties of the cylinder 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 oneterm approximate solutions (or the transient temperature charts) are applicable (this
assumption will be verified).
Properties
The thermal properties of aluminum are given to be
k
= 237 W/m.
°
C and
α
= 9.71
×
10
5
m
2
/s.
Analysis
This semiinfinite cylinder can physically be formed by the intersection of a long cylinder of
radius
r
o
=
D
/2 = 7.5 cm and a semiinfinite medium. The dimensionless temperature 5 cm from the
surface of a semiinfinite medium is first determined from
8951
.
0
1049
.
0
1
)
,
(
1049
.
0
)
7308
.
0
)(
0468
.
1
(
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This note was uploaded on 01/19/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.
 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat

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