Question

In a gas turbine, regenerator is used to preheat the incoming air. Turbine exhaust temperature is 700 K while the ambient air is at 300 K. It is desired to cool the exhaust upto 400 K. Overall heat transfer coefficient is 30 $W/m^{2}K.$
$c_p=1kJ/kgK$
Area of heat transfer in heat exchanger, if mass flow rate is 0.1 kg/s is

Answer 1

(C)

Since in a regeneration system of gas turbine there is same fluid (air) on both side with approximately same mass flow rate and specific heat,

$C_h=C_c=C_{mm}$
$C_h(T_{hi}-T_{ho})=C_c(T_{co}-T_{ci})$
$700-400=T_{co}-300$
$T_{co}=600K$ (i.e. counter flow)

$\epsilon =$\frac{T_{hi}-T_{ho}}{T_{hi}-T_{ci}}=\frac{700-400}{700-300}=0.75\)

$\epsilon =\frac{NTU}{1+NTU}$

$0.75=\frac{NTU}{1+NTU}$

NTU = 3

or $\frac{UA}{C_{min}}=NTU=3$

$A=\frac{3\times 1\times {10}^3\times 0.1}{30}=10m^2$