unsteady heat transfer

1. Heat Transfer chemical and petroleum eng
r z
2L
Multi-Dimensional Unsteady-state Heat Conduction
The Heisler charts are used to obtain the temperature distribution in the infinite plate of
thickness 2L, in the long cylinder, or in the sphere. For the problems in which heat transferred
with more than one dimensional, it is possible to combine the solutions for one-dimensional
systems obtain the solutions for the multidimensional problems.
For the rectangular bar,
or
2
1 2
2 L
i
L
i
bar
i































For short cylinder r,
plate
inite
i
cyl
inite
i
cylM
i inf
.
inf































solid
infinite
-
semi
for
solution
S(x)
plate
infinite
for
solution
P(x)
cylinder
infinite
for
solution
)
(




C
if
The general is

2. Heat Transfer Third Year

3. Heat Transfer Third Year
1
r0=5cm
2L=16
r=5cm
X=8cm
2
Example: A 10cm diameter, 16cm long cylinder with properties: k=0.5 W/m.K and α=5 ×10-
7
m2
/s is initially at a temperature of 20°C. The cylinder is placed in an oven where the
ambient temperature is 500°C, h = 30 W/m2
.K. Determine the min and max temperature in the
cylinder 30min after it has been placed in the oven.
Solution
 
  C
481
500
20
039
.
0
500
039
.
0
155
.
0
249
.
0
C
297
500
20
423
.
0
500
423
.
0
47
.
0
9
.
0
155
.
0
47
.
0
33
.
0
33
3
47
.
0
10
36
.
0
,
33
.
0
)
2
249
.
0
9
.
0
27
.
0
27
9
.
0
21
.
0
,
14
.
0
)
1
sec
1800
30
,
8
16
2
0
0
0
0
0
2
0
0
0
0
2





















































max
cylinder
i
plate
i
combined
i
min
cylinder
i
plate
i
combined
i
i
0
i
0
i
i
0
i
0
i
0
T
θ
θ
θ
θ
θ
θ
e
temperatur
max
The
T
θ
θ
θ
θ
θ
θ
e
temperatur
min
The
θ
θ
θ
θ
θ
θ
0.
θ
θ
,
e 4.1
From figur
4.
figure
From
r
t
hr
k
cylinder
infinite
θ
θ
θ
θ
θ
θ
0.
θ
θ
e 4.12,
From figur
4.9
figure
From
hL
k
L
t
plate
infinite
r
r
L,
x
at
e
temperatur
max
0
r
0,
x
at
e
temperatur
min
60
t
cm
x
L
L





