Solve the following problem:
Q: The wing of an airplane has a polished aluminum skin. At a 1500 m altitude, it absorbs 100 W/m2 by solar radiation. Assuming that the interior surface of the wing's skin is well insulated and the wing has a chord of 6 m length, i.e., L = 6 m, estimate the equilibrium temperature of the wing at a flight speed of 150 m/s at distances of 0.1 m, 1 m, and 5 m from the leading edge. Discuss the effect of a temperature gradient along the chord.
GIVEN
Airplane wing with polished aluminum skin
Altitude = 1500 m
Absorbed solar radiation (qsol/A) = 100 W/m2
Cord length of wing (L) = 6 m
Flight speed (U∞) = 150 m/s
ASSUMPTIONS
Steady state
Inside surface of wing is well insulated, so heat loss from the inner surface is negligible
Radiative loss from the wing surface is negligible
Flight speed given is air speed not ground speed
Variation of air properties with pressure is negligible
Neglect aerodynamic heating
