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Water \((C_p = 4.18\,\text{kJ/kg·K})\) at 80°C enters a counterflow heat exchanger with a mass flow rate of 0.5 kg/s. Air \((C_p = 1\,\text{kJ/kg·K})\) enters at 30°C with a mass flow rate of 2.09 kg/s. If the effectiveness of the heat exchanger is 0.8, the LMTD, in °C, is
- 40
- 20
- 10
- 5
Correct answer: 10
Solution
The minimum heat-capacity rate is for water: \(C_{min}=0.5\times 4.18=2.09\) kW/K. With effectiveness 0.8, the heat transfer is \(Q=0.8\,C_{min}(80-30)=83.6\) kW, which leads to terminal differences of 40°C and 20°C, giving an LMTD of 10°C.
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