A gas consisting of 20% CO 2 and 80% oxygen and nitrogen leaves a lime kiln at

Question:

A gas consisting of 20% CO₂and 80% oxygen and nitrogen leaves a lime kiln at 2000°F and enters a square duct measuring 6 in. by 6 in. in cross section. The specific heat of the gas is 0.28 Btu/lb_m°F, and it is to be cooled to 1000°F in the duct, whose inside surface is maintained at 800°F, and whose walls have an emissivity of 0.9. The mass velocity of the kiln gas is 0.4 lb_m/ft²· s and the convective heat-transfer coefficient between the gas and duct walls is 1.5 Btu/h ft²°F.
a. Determine the required length of duct to cool the gas to 1000°F.
b. Determine the ratio of radiant-energy transfer to that by convection.
c. At what temperature would the gas leave the duct if the length of the duct were twice the value determined in part (a)? (Courtesy of the American Institute of Chemical Engineers.) As the response of the gas to emission and absorption of radiant energy differs, an approximation for the radiantenergy exchange between the enclosure and gas contained within an arbitrary control volume is given by