Heat is transferred by radiation and convection between the inner surface of the nacelle of the wind turbine of Example 1.3 and the outer surfaces of the gearbox and generator. The convection heat flux associated with the gearbox and the generator may be described by q" _conv,gb = h(T_gb  –T_∞) and q"_{conv, gen} = h(T_gen – T_∞), respectively, where the ambient temperature T_∞
≈ T_s (which is the nacelle temperature) and h = 40 W/m² · K. The outer surfaces of both the gearbox and the generator are characterized by an emissivity of ϵ = 0.9. If the surface areas of the gearbox and generator are A_gb = 6 m² and A_gen =  4 m², respectively, determine their surface temperatures.

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 η_gb = 0.93. In turn, the gearbox output shaft drives an electric generator with an efficiency of η_gen = 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_sur = 20°C, respectively, determine the minimum possible operating temperature inside the nacelle. The emissivity of the nacelle is ϵ = 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.

Transcribed Image Text:

Air Tsur T = 25°C = 20°C Hub h = 35 W/m2.K - L = 6 m ↑ D = 3 m T,,E = 0.83 Generator, = ngen = 0.95 = 0.93 Gearbox, 7gb Nacelle