Common practice in processing plants is to clad pipe insulation with an aluminum foil coating to prevent heat losses by radiation. because of dust and other pollutants in the air, the aluminum foil surface, which is initially bright, will become dull with time. typically, the emissivity might change from 0.10 at installation to 0.36 with extended service. for a 300-mm diameter foil-covered pipe whose surface temperature is 90°c, determine the fraction of heat loss from the pipe due to radiation before and after dulling of the foil. consider two cases with surrounding and ambient air at 25°c: (a) quiescent air and (b) a cross wind velocity of 10 m/s. assume the pipe is horizontal and sees only the sky at tsky-18°c