In a plate heat exchanger, the heat capacity rates of the hot and cold fluid streams are equal ($C_{hot} = C_{cold} = C_{min} = 10.0\text{ kW/K}$). If the Number of Transfer Units $NTU = 2.0$, using the counter-flow effectiveness formula $\epsilon = \frac{NTU}{1 + NTU}$ (for $C_{min}/C_{max} = 1$), the heat exchanger effectiveness $\epsilon$ is ________ (round off to 3 decimal places).
Answer Key:
0.667
Step-by-Step Solution & Explanation
For a counter-flow heat exchanger with equal heat capacity rates ($C_r = 1.0$):
$\epsilon = \frac{NTU}{1 + NTU}$
Given $NTU = 2.0$:
$\epsilon = \frac{2.0}{1 + 2.0} = \frac{2}{3} \approx 0.6667 \approx 0.667$