problem4-57 - PROBLEM 4.57 KNOWN: Dimensions and operating...

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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) Steady-state, two-dimensional 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 1c-6c, 1o-6o, and 1i-6i. 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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problem4-57 - PROBLEM 4.57 KNOWN: Dimensions and operating...

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