GATE 2020 CH – Question 51

Heat Transfer · Heat exchangers and evaporators: types and design · 2 marks · Numerical answer

In a countercurrent double-pipe heat exchanger, cold fluid warms from 40°C to 60°C while hot fluid cools from 100°C to 70°C. Find LMTD in °C, to two decimal places.

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Correct answer: 34.20 to 35.20

Explanation

The countercurrent terminal differences pair hot inlet with cold outlet and hot outlet with cold inlet: $\Delta T_1=100-60=40$ K and $\Delta T_2=70-40=30$ K. Thus $\Delta T_{lm}=(40-30)/\ln(40/30)=34.7606$ K. A temperature difference has the same numerical value in °C, giving 34.76°C.

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