5.53 To increase the thermal efficiency of a gas turbine cycle, the combustion air is often preheated using the hot gases exhausting the turbine. Consider the case where this is being accomplished using a cross-flow (unmixed–unmixed) heat exchanger, as shown in Figure P5.53. Hot combustion gases exit the turbine at a mass flow rate of 51,600 lbm/h with a temperature of 850°F. Air enters the compressor at 1 atm, 70°F, with a mass flow rate of 49,200 lbm/h. The pressure ratio across the compressor is PR = 8 and the isentropic efficiency of the compressor is 85%. The overall heat transfer coefficient for the heat exchanger has been found to be U = 17.6 Btu/h·ft2·°F. If the combustion air is to be preheated to 700°F, determine the total heat exchange area required for this CFHX (ft2).

Assume that the pressure drops through the connecting lines and the heat exchangers are negligible and that the working fluid can be modeled as air throughout the cycle.