Question

The exhaust-gas temperature leaving a continuously operating furnace is 260°C, and a proposal is being considered to install a heat exchanger in the exhaust-gas stream to generate low-pressure steam at 105°C. the question to be investigate is whether it is economical to install such a heat exchanger, and if so, to find its optimum size. The following data apply:
Table
year factor year factor year factor
1 0 8 3.008 15 5.275
2 0.476 9 3.376 16 5.552
3 0.937 10 3.730 17 5.801
4 1.379 11 4.060 18 6.058
5 1.810 12 4.384 19 6.295
6 2.224 13 4.696 20 6.5
7 2.622 14 5.002 21 6.703

Flow of exhaust gas-----7.5kg/s
Specific heat of exhaust gas---1.05kJ/(kg*k)
Value of the heat in the form of steam---$1.5 per gigajoule
U value of heat exchanger based on gas-side area---23W/(m^2*K)
Cost of the heat exchanger including installation based on gas-side area----$90 per square meter
Interest rate----8%
Life of installation----5years
Saturated liquid water enters heat exchanger at 105°C and leaves as saturated vapor

1) Develop the equation for the saving as a function of the area, expressed as a uniform annual amount.