GATE 2024 BT – Question 54

Fundamentals of Biological Engineering · Upstream Processing: Media formulation and optimization, sterilization of air and media · 2 marks · Numerical answer

Fermentation medium is cooled from 121 $^o$C to 30 $^o$C in a double pipe heat exchanger. If cold water is flowing in the counter-current direction and is heated from 10 $^o$C to 70 $^o$C, then the Log-Mean Temperature Difference (LMTD) is ________ $^o$C (rounded off to the nearest integer).

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Correct answer: 33

Explanation

Counter-current: $\Delta T_1 = 121 - 70 = 51$ and $\Delta T_2 = 30 - 10 = 20$. $LMTD = \frac{51 - 20}{\ln(51/20)} = \frac{31}{0.936} = 33$ $^o$C.