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PROBLEM 4.57
KNOWN:
Dimensions and operating conditions for a gas turbine blade with embedded channels.
F
IND:
Effect of applying a zirconia, thermal barrier coating.
SCHEMATIC:
ASSUMPTIONS:
(1) Steadystate, twodimensional conduction, (2) Constant properties, (3) Negligible
adiation.
r
ANALYSIS:
Preserving the nodal network of Example 4.4 and adding surface nodes for the TBC, finite
difference equations previously developed for nodes 7 through 21 are still appropriate, while new
equations must be developed for nodes 1c6c, 1o6o, and 1i6i.
Considering node 3c as an example, an
energy balance yields
()
( )
cc
c
o
,
o
3
c2
c
3
c4
c
3
c
3
o
c
ky
2
2
kx
h
x
T
T
TT
xx
y
∞
ΔΔ
Δ
Δ−
+
−
+
−
+
−
Δ
3
c
0
=
o
r, with
Δ
x = 1 mm and
Δ
y
c
= 0.5 mm,
oo
2c
4c
3o
3c
,o
hx
0.25 T
T
2T
2.5
T
T
kk
∞
++−+
=
−
⎛⎞
⎜⎟
⎝⎠
S
imilar expressions may be obtained for the other 5 nodal points on the outer surface of the TBC.
Applying an energy balance to node 3o at the inner surface of the TBC, we obtain
( )
c
3c
3o
2o
3o
4o
3o
3i
3o
ct
2
2
x
yx
x
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 Spring '10
 LEE,J.S.
 Heat Transfer

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