PROBLEM 3.116KNOWN:Dimensions and thermal conductivity of a gas turbine blade. Temperature and convectioncoefficient of gas stream. Temperature of blade base and maximum allowable blade temperature.FIND:(a) Whether blade operating conditions are acceptable, (b) Heat transfer to blade coolant.SCHEMATIC:ASSUMPTIONS:(1) One-dimensional, steady-state conduction in blade, (2) Constant k, (3) Adiabaticblade tip, (4) Negligible radiation.ANALYSIS:Conditions in the blade are determined by Case B of Table 3.4.(a) With the maximum temperature existing at x = L, Eq. 3.75 yields()bTL T1TTcoshmL∞∞−=−( )1/2242cmhP/kA250W/mK 0.11m/20W/m K 6 10
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