Example 1.3 The blades of a wind turbine turn a large shaft at a relatively slow speed. The rotational speed is increased by a gearbox that has an efficiency of 0.93. In turn, the gearbox output shaft drives an electric generator with an efficiency of 0.95. The cylindrical nacelle, which houses the gearbox, generator, and associated equipment, is of length L = 6 m and diameter D= 3 m. If the turbine produces P = 2.5 MW of electrical power, and the air and surroundings temperatures are T = 25 °C and Tur = 20 °C, respectively, determine the minimum possible operating temperature inside the nacelle. The emissivity of the nacelle is 0.83, and the convective heat transfer coefficient is h = 35 W/m² .K. The surface of the nacelle that is adjacent to the blade hub can be considered to be adiabatic, and solar irradiation may be neglected. Note: The solution is to use N number of fins or fins to reduce the maximum church to less than 143 °C and compare the solution before and after using fins Tu-20°C T-25°C Hub -35 W/m².K 3m T₁-0.83 Generator, -0.5 Gearbox,-0.93 -Nacelle

Example 1.3 The blades of a wind turbine turn a large shaft at a relatively slow speed. The rotational speed is increased by a gearbox that has an efficiency of 0.93. In turn, the gearbox output shaft drives an electric generator with an efficiency of 0.95. The cylindrical nacelle, which houses the gearbox, generator, and associated equipment, is of length L = 6 m and diameter D= 3 m. If the turbine produces P = 2.5 MW of electrical power, and the air and surroundings temperatures are T = 25 °C and Tur = 20 °C, respectively, determine the minimum possible operating temperature inside the nacelle. The emissivity of the nacelle is 0.83, and the convective heat transfer coefficient is h = 35 W/m² .K. The surface of the nacelle that is adjacent to the blade hub can be considered to be adiabatic, and solar irradiation may be neglected. Note: The solution is to use N number of fins or fins to reduce the maximum church to less than 143 °C and compare the solution before and after using fins Tu-20°C T-25°C Hub -35 W/m².K 3m T₁-0.83 Generator, -0.5 Gearbox,-0.93 -Nacelle

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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Question

Example 1.3
The blades of a wind turbine turn a large shaft at a relatively slow speed. The rotational speed
is increased by a gearbox that has an efficiency of 0.93. In turn, the gearbox output shaft
drives an electric generator with an efficiency of 0.95. The cylindrical nacelle, which houses
the gearbox, generator, and associated equipment, is of length L = 6 m and diameter D = 3 m.
If the turbine produces P = 2.5 MW of electrical power, and the air and surroundings
temperatures are T = 25 °C and T = 20 °C, respectively, determine the minimum possible
operating temperature inside the nacelle. The emissivity of the nacelle is 0.83, and the
convective heat transfer coefficient is h = 35 W/m² .K. The surface of the nacelle that is
adjacent to the blade hub can be considered to be adiabatic, and solar irradiation may be
neglected.
Note: The solution is to use N
number of fins or fins to reduce the
maximum church to less than 143 °C
and compare the solution before and
after using fins
Air
Tur -20ºC
T-25°C
Hub
-35 W/m2.K
2-6m
D-3m
T₁-0.83
Generator, -0.95
Gearbox,-0.93
Nacelle

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