Question 9.29: A flow of 1 kg/s of an organic liquid of heat capacity 2.0 k......
A flow of 1 kg/s of an organic liquid of heat capacity 2.0 kJ/kg K is cooled from 350 to 330 K by a stream of water flowing countercurrently through a double-pipe heat exchanger. Estimate the effectiveness of the unit if the water enters the exchanger at 290 K and leaves at 320 K.
Heat load, Q = 1 x 2.0(350 – 330) = 40 kW
Flow of water. G_{\mathrm{cool}}={\frac{40}{4.187(320-290)}}=0.318{\mathrm{~kg/s}}
For organic: (G C_{p})_{\mathrm{hot}}=(1\times2.0)=2.0\mathrm{~kW/K~(=G_{2}C_{p_{2}})}
For water: (G C_{p})_{\mathrm{cold}}=(0.318\times4.187)=1.33\;{\mathrm{kW/K(}}= G C_{p})_{\mathrm{min}}\;=(G_{1}C_{p_{1}})
From equation 9.235:
\eta=\frac{G_{2}C_{p_{2}}(T_{22}-T_{21})}{G_{1}C_{p_{1}}(T_{11}-T_{21})} (9.235)
effectiveness \eta={\frac{2.0(350-330)}{1.33(350-290)}}
= \underline{\underline{0.50}}