A counterflow regenerator is used in a gas turbine power plant to preheat the air before it enters the combustor. The air leaves the compressor at a temperature of 350°C. Exhaust gas leaves the turbine at 700°C. The mass flow rates of air and gas are 5 kg/s. Take the cp of air and gas to be equal to 1.05 kJ/(kg K). Determine the required heat transfer area as a function of the regenerator effectiveness, if the overall heat transfer coefficient is 75 W/(m2 K).

Question

GIVEN

• Counterflow air-to-gas heat exchanger

• Entering temperatures

? Ta,in = 350°C

? Tg,in = 700°C

• Mass flow rates: m a= 5 kg/s

• Specific heats: cpa = cpg = 1.05 kJ/(kg K) = 1050 J/(kg K)

• Overall heat transfer coefficient (U) = 75 W/(m2 K)

FIND

• The heat transfer area (A) as a function of the effectiveness (e)

SKETCH

Answer 1

Since ma cpa = mg cpg, the temperature difference between the gas and air remain constant and ?T = Tg,in Ta,out . The heat capacity rates are equal, therefore reduces to



Substituting this into the expression for area



This is tabulated and plotted below



COMMENTS

This problem can also be solved by calculating the number of transfer units for a given area then reading the effectiveness off