Chapter 4
Transient Heat Conduction
484
A cylindrical aluminum block is heated in a furnace. The length of time the block should be kept in
the furnace and the amount of heat transferred to the block are to be determined.
Assumptions
1
Heat conduction in the cylindrical block is twodimensional, and thus the temperature
varies in both axial
x
 and radial
r
directions.
2
Heat transfer from the bottom surface of the block is
negligible.
3
The thermal properties of the aluminum are constant.
4
The heat transfer coefficient is
constant and uniform over the entire surface.
5
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 the aluminum block are given to be
k
= 236 W/m.
°
C,
ρ
= 2702 kg/m
3
,
C
p
= 0.896 kJ/kg.
°
C, and
α
= 9.75
×
10
5
m
2
/s.
Analysis
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat, Heat Transfer, TI, Thermal conductivity

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