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Chapter 4
Transient Heat Conduction
481
A cubic block and a cylindrical block are exposed to hot gases on all of their surfaces. The center
temperatures of each geometry in 10, 20, and 60 min are to be determined.
Assumptions
1
Heat conduction in the cubic block is threedimensional, and thus the temperature varies in
all
x
,
y
, and
z
 directions.
2
Heat conduction in the cylindrical block is twodimensional, and thus the
temperature varies in both axial
x
 and radial
r
directions.
3
The thermal properties of the granite 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 granite are given to be
k
= 2.5 W/m.
°
C and
α
= 1.15
×
10
6
m
2
/s.
Analysis
:
Cubic block:
This cubic block can physically be formed by the intersection of three infinite plane walls of
thickness 2
L
= 5 cm.
After 10 minutes
: The Biot number, the corresponding constants, and the Fourier number are
400
.
0
)
C
W/m.
5
.
2
(
)
m
025
.
0
)(
C
.
W/m
40
(
2
=
°
°
=
=
k
hL
Bi
⎯→
⎯=
=
λ
11
05932
10580
..
and
A
τ
α
==
××
=>
−
t
L
2
6
115 10
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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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