GATE 2026 CH – Question 52
In a double pipe cocurrent heat exchanger, operating at steady state, oil (specific heat capacity = 2100 J kg$^{-1}$ °C$^{-1}$) entering at 7 kg s$^{-1}$ at 100 °C is used to heat water (specific heat capacity = 4200 J kg$^{-1}$ °C$^{-1}$) flowing at 3.5 kg s$^{-1}$ from 20 °C to 50 °C. If the overall heat transfer coefficient is 291 W m$^{-2}$ °C$^{-1}$, the required heat transfer area (in m$^2$) is _____ (rounded off to one decimal place).
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Correct answer: 34.82 to 35.18
Explanation
The heat duty is $Q = 3.5 \times 4200 \times 30 = 441000$ W. The oil outlet temperature is $100 - \frac{441000}{7 \times 2100} = 70$ °C. For cocurrent flow, $\Delta T_1 = 100 - 20 = 80$ °C and $\Delta T_2 = 70 - 50 = 20$ °C, so $\Delta T_{lm} = \frac{80 - 20}{\ln 4} = 43.28$ °C. Then $A = \frac{Q}{U\Delta T_{lm}} = \frac{441000}{291 \times 43.28} = 35.0$ m$^2$.