2. 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 investigated is whether it is economical to install such a heat exchanger, and, if so, to find its optimum size. The following data apply: Flow of exhaust gas, 7.5 kg/s. Specific heat of exhaust gas, 1.05 kJ/(kg K). Value of the heat in the form of steam, $1.50 per gigajoule. U value of heat exchanger based on gas-side area, 23 W/(m² K). Cost of the heat exchanger including installation based on gas-side area, $90 per square meter. Interest rate, 8 percent. Life of installation, 5 years. Saturated liquid water enters heat exchanger at 105°C and leaves as saturated vapor. 1 of 3 (a) Develop the equation for the savings as a function of the area, expressed as a uniform annual amount. (b) What is the maximum permitted area if the exit-gas temperature is to be above 120°C in order to prevent condensation of water vapor from the exhaust gas? (c) (c) Use a seven-point Fibonacci search and set up a table to simplify calcu- lation of the optimum heat-transfer area.