GATE 2016 ME (ME2) – Question 52
Consider a parallel-flow heat exchanger with area 𝐴p and a counter-flow heat exchanger with area 𝐴c. In both the heat exchangers, the hot stream flowing at 1 kg/s cools from 80 °C to 50 °C. For the cold stream in both the heat exchangers, the flow rate and the inlet temperature are 2 kg/s and 10 °C, respectively. The hot and cold streams in both the heat exchangers are of the same fluid. Also, both the heat exchangers have the same overall heat transfer coefficient. The ratio 𝐴c/𝐴p is _________
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Correct answer: 0.91 to 0.95
Explanation
Energy balance with equal specific heats gives cold outlet10+(1/2)(80−50)=25°C. Parallel terminal differences are70 and25K, giving LMTDp=45/ln(70/25). Counterflow differences are55 and40K, giving LMTDc=15/ln(55/40). Equal Q and U imply Ac/Ap=LMTDp/LMTDc=**0.92788**.