Chapter 12, Problem 12.128P

The oxidized-aluminum wing of an aircraft has a chord length of Lc ◰ 4 m and a spectral, hemispher- ical emissivity characterized by the following distribution.

(a)Consider conditions for which the plane is on the ground where the air temperature is ${27}^{\circ }C$ , the solar irradiation is ${\text{800 W/m}}^2$ , 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 temperatureare $-{40}^{\circ }C,1100{\text{ W/m}}^2\text{ and 235K}$ , respectively. What is the temperature of the wing’s top surface? The properties of the air may be approximated as $\rho =0.470{\text{ kg/m}}^3,\mu \text{=1}{\text{.50x10}}^{-5}N\cdot s/m^2,K=0.021\text{ W/m}\cdot \text{K, and Pr =0}\text{.72}$ .