Chapter 9, Problem 9.72P

A bituminous coal is burned with air in a boiler furnace. The coal is fed at a rate of 40,000 kg/h and has an ultimate analysis of 76wt% C, 5% H. 8% O, negligible amounts of N $\left(-\stackrel{\dot{}}{Q}\right)$and S, and 11% noncombustible ash (see Problem 9.58), and a higher heating value of 25,700 kJ/kg. Air enters a preheater at 30°C and 1 atm with a relative humidity of 30%, exchanges heat with the hot flue gas leaving the furnace, and enters the furnace at temperature T_a(°C). The flue gas contains 7.71 mole% CO₂and 1.29 mole% CO on a dry basis, and the balance is a mixture of O₂, N₂, and H₂O. It emerges from the furnace at 260°C and is cooled to 150°C in the preheater. Noncombustible residue {slag) leaves the furnace at 450°C and has a heat capacity of 0.97 kJ/(kg·°C).

1. Prove that the air-to-fuel ratio is 16.1 standard cubic meters/kg coal and that the flue gas contains 4.6% H₂O by volume.
2. Calculate the rate of cooling required to cool the flue gas from 260°C to 150°C and the temperature to which the air is preheated. {Note: A trial-and-error calculation is required.)
3. If 60% of the heat transferred from the furnace goes into producing saturated steam at 30 bar from liquid boiler feedwater at 50°C, at what rate (kg/h) is steam generated?