A small sphere (1 in. diam) is placed in a heating oven whose cavity is a 1

Question:

A small sphere (1 in. diam) is placed in a heating oven whose cavity is a 1 ft cube filled with air at 14.7 psia, contains 3 per cent water vapor at 1000?F, and whose walls are at 2000?F. The emissivity of the sphere is equal to 0.4 ?? 0.0001 T, where T is the surface temperature in ?F. When the surface temperature of the sphere is 1000?F, determine(a) The total irradiation received by the walls of the oven from the sphere,(b) The net heat transfer by radiation between the sphere and the walls of the oven, and(c) The radiant heat transfer coefficient.GIVENA small sphere in a 1 ft cubic heat oven filled with airSphere diameter (D) = 1 in ?? 1/12 ftAir pressure = 14.7 psia = 1 atmAir contains 3% water vaporAir temperature (Tm) = 1000?FOven wall temperature (T2) = 2000?F = 2460 RSphere emissivity (ε1) = 0.4 ?? 0.0001 T (T in ?F)Sphere surface temperature (T1) = 1000 = 1460 RASSUMPTIONSThe gas is a gray bodyThe oven walls are black (ε2 = 1)The sphere is near the center of theoven