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1.
A flue passing hot exhaust gases has a square cross section, 300 mm to a side.
The
walls are constructed of refractory brick 150 mm thick with a thermal conductivity
of 0.85 W/m•K.
Use a grid spacing of 75 mm.
The outer wall is held at 25°C while
the inner wall is held at 350°C.
(a) From a finite control volume, derive the finitedifference equation for a two
dimensional steady interior point without energy generation.
Clearly sketch the
control volume, labelling the nodes and the heat transfer rates.
(b) Determine the steadystate temperature distribution.
(a)
st
out
gen
in
E
E
E
E
=

+
0
E
E
out
in
=

(m, n)
(m, n1)
(m1, n)
(m+1, n)
(m, n+1)
L
x
y
0
q
q
q
q
)
1
n
,
m
(
)
n
,
m
(
)
n
,
1
m
(
)
n
,
m
(
)
n
,
m
(
)
1
n
,
m
(
)
n
,
m
(
)
n
,
1
m
(
=


+
+
→
+
→
→

→

0
y
Δ
T
T
xL
Δ
k
x
Δ
T
T
yL
Δ
k
y
Δ
T
T
xL
Δ
k
x
Δ
T
T
yL
Δ
k
n
,
m
1
n
,
m
n
,
m
n
,
1
m
1
n
,
m
n
,
m
n
,
1
m
n
,
m
=

+

+




+
+


0
T
T
T
T
T
T
T
T
n
,
m
1
n
,
m
n
,
m
n
,
1
m
1
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 Fall '08
 Kuznetsov
 Heat Transfer

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