Consider a recuperative cross-flow heat exchanger (both fluids unmixed) used in a gas turbine system that carries the exhaust gases at a flow rate of 7.5 kg/s and a temperature of 500°C. The air initially at 30°C and flowing at a rate of 15 kg/s is to be heated in the recuperator. The convective heat transfer coefficients on the exhaust gas and air side are 750 W/m²·K and 300 W/m²·K, respectively. Due to longterm use of the gas turbine, the recuperative heat exchanger is subject to fouling on both gas and air side that offers a resistance of 0.0004 m²·K/W each. Take the properties of exhaust gas to be the same as that of air (c_p= 1069 J/kg·K). If the exit temperature of the exhaust gas is 320°C, determine

(a) If the air could be heated to a temperature of 150°C,

(b) The area of heat exchanger,

(c) If the answer to part (a) is no, then determine what should be the air mass flow rate in order to attain the desired exit temperature of 150°C,

(d) Plot variation of the exit air temperature over a temperature range of 75°C to 300°C with air mass flow rate assuming all the other conditions remain the same.

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Gas flow (unmixed) Alr flow (unmixed)