Solve the following problem:
Q: A turbine blade 6.3 cm long, with cross-sectional area A = 4.6 ×10-4 m2 and perimeter P = 0.12 m, is made of stainless steel (k = 18 W/(m K). The temperature of the root, Ts, is 428°C. The blade is exposed to a hot gas at 871°C, and the heat transfer coefficient h is 454 W/(m2 K). Determine the temperature of the blade tip and the rate of heat flow at the root of the blade. Assume that the tip is insulated.
GIVEN
Stainless steel turbine blade
Length of blade (L) = 6.3 cm = 0.063 m
Cross-sectional area (A) = 4.6 × 10-4 m2
Perimeter (P) = 0.12 m
Thermal conductivity (k) = 18 W/(m K)
Temperature of the root (Ts) = 482°C
Temperature of the hot gas (T∞) = 871°C
Heat transfer coefficient ( hc ) = 454 W/(m2 K)
ASSUMPTIONS
Steady state conditions prevail
The thermal conductivity is uniform
The tip is insulated
The cross-section of the blade is uniform
One dimensionalconduction
