A re-cooperator is a heat exchanger that heats air used in a combustion process by extracting energy

Question:

A re-cooperator is a heat exchanger that heats air used in a combustion process by extracting energy from the products of combustion. It can be used to increase the efficiency of a gas turbine by increasing the temperature of air entering the combustor. Consider a system for which the re-cooperator is a cross-flow heat exchanger with both fluids unmixed and the flow rates associated with the turbine exhaust and the air are m_h = 6.5 kg/s and m_c = 6.2 kg/s, respectively. The corresponding value of the overall heat transfer coefficient is U = 100 W/m² ? K.

(a) If the gas and air inlet temperatures are T_h,i = 700 K and T_c,i = 300 K, respectively, what heat transfer surface area is needed to provide an air outlet temperature of T_c,o = 500 K? Both the air and the products of combustion may be assumed to have a specific heat of 1040 J/kg ? K.

(b) For the prescribed conditions, compute and plot the air outlet temperature as a function of the heat transfer surface area.