A flag pole made of solid aluminum is 20 feet tall and one inch in diameter. The pole is situated in full sunlight, and the arriving solar energy is 310 watts per square meter of the surface on which the solar photons are incident. The pole is painted black and absorbs 95% of the energy that is incident upon it. The wind is strong so that the heat transfer coefficient h for convection is 20.9 W/m^2-K, and the temperature of the air is 29.2 C. The rate at which the emitted photons carry energy away is given by Energy Rate [W] = 5.4*10^-8*T^4*A where T is temp of the pole in Kelvin and A is the surface area of flag pole which radiation is emitted.
Using the First Law of Thermodynamics you get Q(dot) = 0.
Net rate of heat inflow = 0 = rate at which solar energy is absorbed - rate at which radiant energy leaves - rate at which convection extracts heat
Solar energy is not able to wrap around a pole, but radiant energy is emitted uniformly from the entire surface of the pole. Convection extracts heat from the entire surface of the pole. Be careful to work this problem in Kelvin rather than Celsius.
What is the equilibrium temperature of the flag pole?