GATE 2025 BT – Question 61
A hot, freshly-sterilised fermentation medium is cooled in a double-pipe heat-exchanger. The medium enters the inner pipe of the exchanger at 95 $^o$C and leaves the exchanger at 40 $^o$C. Cooling water, flowing counter-currently to the medium, enters the annulus of the exchanger at 15 $^o$C and leaves the exchanger at 45 $^o$C. The overall heat transfer coefficient is 1350 W m$^{-2}$ $^o$C$^{-1}$. The rate of heat transfer per unit area will be _______ W/m$^2$. (Round off to the nearest integer)
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Correct answer: 48691
Explanation
In counter-current flow the hot inlet (95) meets the cold outlet (45) and the hot outlet (40) meets the cold inlet (15), so $\Delta T_1 = 50$ and $\Delta T_2 = 25$. The log-mean temperature difference is $\frac{50 - 25}{\ln 2} = 36.07$ $^o$C. The heat transfer per unit area is $U\Delta T_{lm} = 1350 \times 36.07 = 48691$ W/m$^2$.