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Turbine blades mounted to a rotating disc in a gas turbine engine are exposed to a gas stream that is at T = 1300°C and maintains a convection coefficient of h = 250 W/m².K over the blade. The blades, which are fabricated from Inconel, k 20 W/m-K, have a length of L = 50 mm. The blade profile has a uniform cross-sectional area of A = 6 x 10-4 m² and a perimeter of P = 110 mm. A proposed blade-cooling scheme, which involves routing air through the supporting disc, is able to maintain the base of each blade at a temperature of T, = 300°C. (a) If the maximum allowable blade temperature is 1050°C and the blade tip may be assumed to be adiabatic, is the proposed cooling scheme satisfactory? (b) For the proposed cooling scheme, what is the rate at which heat is transferred from each blade to the coolant, W? 9b = i W Gas stream To h Air coolant Blade tip -Tb -Rotating disk

Turbine blades mounted to a rotating disc in a gas turbine engine are exposed to a gas stream that is at T = 1300°C and maintains a convection coefficient of h = 250 W/m².K over the blade. The blades, which are fabricated from Inconel, k 20 W/m-K, have a length of L = 50 mm. The blade profile has a uniform cross-sectional area of A = 6 x 10-4 m² and a perimeter of P = 110 mm. A proposed blade-cooling scheme, which involves routing air through the supporting disc, is able to maintain the base of each blade at a temperature of T, = 300°C. (a) If the maximum allowable blade temperature is 1050°C and the blade tip may be assumed to be adiabatic, is the proposed cooling scheme satisfactory? (b) For the proposed cooling scheme, what is the rate at which heat is transferred from each blade to the coolant, W? 9b = i W Gas stream To h Air coolant Blade tip -Tb -Rotating disk

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Turbine blades mounted to a rotating disc in a gas turbine engine are exposed to a gas stream that is at T = 1300°C and maintains a convection coefficient of h = 250 W/m².K over the blade. The blades, which are fabricated from Inconel, k 20 W/m-K, have a length of L = 50 mm. The blade profile has a uniform cross-sectional area of A = 6 x 104 m² and a perimeter of P = 110 mm. A proposed blade-cooling scheme, which involves routing air through the supporting disc, is able to maintain the base of each blade at a temperature of Tb = 300°C. (a) If the maximum allowable blade temperature is 1050°C and the blade tip may be assumed to be adiabatic, is the proposed cooling scheme satisfactory? (b) For the proposed cooling scheme, what is the rate at which heat is transferred from each blade to the coolant, W? 9b i W || Gas stream Th Air coolant Blade tip -T₂ - Rotating disk
Transcribed Image Text:Turbine blades mounted to a rotating disc in a gas turbine engine are exposed to a gas stream that is at T = 1300°C and maintains a convection coefficient of h = 250 W/m².K over the blade. The blades, which are fabricated from Inconel, k 20 W/m-K, have a length of L = 50 mm. The blade profile has a uniform cross-sectional area of A = 6 x 104 m² and a perimeter of P = 110 mm. A proposed blade-cooling scheme, which involves routing air through the supporting disc, is able to maintain the base of each blade at a temperature of Tb = 300°C. (a) If the maximum allowable blade temperature is 1050°C and the blade tip may be assumed to be adiabatic, is the proposed cooling scheme satisfactory? (b) For the proposed cooling scheme, what is the rate at which heat is transferred from each blade to the coolant, W? 9b i W || Gas stream Th Air coolant Blade tip -T₂ - Rotating disk
Expert Solution
Step 1

To find:

(a) Whether the  the proposed cooling scheme satisfactory or not if  the maximum allowable blade temperature is 1050°C.

(b) The rate at which heat is transferred for purposed cooling system.

Given:

The temperature is T∞=1300°C.

The convective heat transfer coefficient is h=250 W/m2·K.

The thermal conductivity is k=20 W/m·K.

The length is L=50 mm.

The area is Ac=6×10-4 m2.

The perimeter is P=110 mm.

The blade temperature is Tb=300°C.

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