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 Tsur = 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. Use Fin or N number of fins to reduce the T, of the nacelle less than 143 °C Air Tur-20°C T-25°C Hub h-35 W/m2.K L-6m D-3m T₂,-0.83 Generator, gan 0.95 Gearbox, b-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 Tsur = 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. Use Fin or N number of fins to reduce the T, of the nacelle less than 143 °C Air Tur-20°C T-25°C Hub h-35 W/m2.K L-6m D-3m T₂,-0.83 Generator, gan 0.95 Gearbox, b-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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A fluid is a substance that is continuously deformed by the application of shear stress. The rate of deformation of a fluid depends on its viscosity. The fluid tries to flow when it interacts with some other system.

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 Tsur = 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.
Use Fin or N number of fins to reduce the T, of the
nacelle less than 143 °C
Air
Tsur-20°C
T-25°C
Hub
h-35 W/m².K
-L=6m
D-3m
T₁-0.83
Generator, gen-0.95
Gearbox, gb -0.93
Nacelle

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