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 76 wt% C, 5% H, 8% 0, negligible amounts of N and S. and 11% noncombustible ash (see Problem 9.49), and a higher heating value of 25,700 kJ/kg. Air enters a pre-heater 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 Ta(°C). The flue gas contains 7.71 mole% CO2 and 1.29 mole% CO on a dry basis, and the balance a mixture of O2, N2, and H20. It emerges from the furnace at 260°C and is cooled to 150°C in the pre-heater. Noncombustible residue (slag) leaves the furnace at 450°C and has a heat capacity of 0.97 kJ/ (kg·°C).

(a) 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.

(b) 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.)

(c) If 60% of the heat transferred from the furnace (-Q) goes into producing saturated steam at 30 bar from liquid boiler feed water at 50°C, at what rate (kg/h) is steam generated?