Chapter 1, Problem 1.43P

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 $q_{\text{conv}.\text{gb}}^{"}=h\left(T_{gb}-T_{\infty }\right)$ and $q_{\text{conv}.\text{gen}}^{"}=h\left(T_{gen}-T_{\infty }\right),$ respectively, where the ambient temperature $T_{\infty }\approx T_s$ (which is the nacelle temperature) and $h=40{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ The outer surfaces of both the gearbox and the generator are characterized by an emissivity of $\epsilon =\mathrm{0.9.}$ If the surface areas of the gearbox and generator are $A_{\text{gb}}=6{\text{m}}^{\text{2}}$ and $A_{\text{gen}}=4{\text{m}}^{\text{2}},$ respectively, determine their surface and A temperatures.