GATE 2025 CH – Question 51
Water flowing at 70 kg/min is heated from 25 °C to 65 °C in a counter-flow double pipe heat exchanger using hot oil. The oil enters at 110 °C and exits at 65 °C. If the overall heat transfer coefficient is 300 W/(m$^2$ K), the heat exchanger area is ____ m$^2$ (rounded off to 1 decimal place).
GIVEN: Specific heat of water and oil are 4.2 kJ/(kg °C) and 2 kJ/(kg °C), respectively.
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Correct answer: 15.32 to 15.48
Explanation
The heat duty is $Q = \frac{70}{60} \times 4200 \times (65 - 25) = 196000$ W. For counter flow the end differences are $\Delta T_1 = 110 - 65 = 45$ °C and $\Delta T_2 = 65 - 25 = 40$ °C, so $\Delta T_{lm} = \frac{45 - 40}{\ln(45/40)} = 42.45$ °C. Then $A = \frac{Q}{U\Delta T_{lm}} = \frac{196000}{300 \times 42.45} = 15.4$ m$^2$.