The oxidized-aluminum wing of an aircraft has a chord length of L_c = 4 m and a spectral, hemispherical emissivity characterized by the following distribution.

  (a) Consider conditions for which the plane is on the ground where the air temperature is 27°C, the solar irradiation is 800 W/m², and the effective sky temperature is 270 K. If the air is quiescent, what is the temperature of the top surface of the wing? The wing may be approximated as a horizontal, flat plate.

  (b) When the aircraft is flying at an elevation of approximately 9000 m and a speed of 200 m/s, the air temperature, solar irradiation, and effective sky temperature are -40°C, 1100 W/m², and 235 K, respectively. What is the temperature of the wing's top surface? The properties of the air may be approximated as ρ = 0.470 kg/m³, μ = 1.50 × 10^-5 N. s/m², k = 0.021 W/m. K , and Pr = 0.72.