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Chapter 5
Numerical Methods in Heat Conduction
The upper limit of the time step
Δ
t
is determined from the stability criteria that requires the
coefficient of
in the
T
expression (the primary coefficient) be greater than or equal to zero for all
nodes. The smallest primary coefficient in the 8 equations above is the coefficient of
T
in the
expression since it is exposed to most convection per unit volume (this can be verified), and thus the
stability criteria for this problem can be expressed as
T
m
i
m
i
+
1
i
3
T
i
3
1
+
14 4
0
1
41
4 1
2
−−
≥ →
≤
+
→≤
+
ττ
τ
α
hl
kh
l
k
t
l
hl k
(/
)
)
Δ
since
. Substituting the given quantities, the maximum allowable value of the time step is
determined to be
τα
=Δ
tl
/
2
s
3
.
16
C)]
W/m.
15
/(
m)
015
.
0
)(
C
.
W/m
80
(
1
/s)[
m
10
2
.
3
(
4
)
m
015
.
0
(
2
2
6
2
=
°
°
+
×
≤
Δ
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This note was uploaded on 01/22/2012 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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