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GATE 2025 Chemical Engineering, Q51 · Heat Transfer

The correct answer is 15.2 to 15.6.

Question

Water flowing at 70 kg/min is heated from 25°C25°C to 65°C65°C in a counter-flow double pipe heat exchanger using hot oil. The oil enters at 110°C110°C and exits at 65°C.65°C. If the overall heat transfer coefficient is 300W/(m2K),300 W/(m²K), the heat exchanger area is ____ m2m² (rounded off to 1 decimal place). Given: specific heat of water and oil are 4.2kJ/(kg⋅°C)4.2 kJ/(kg\cdot °C) and 2kJ/(kg⋅°C),2 kJ/(kg\cdot °C), respectively.

Official answer: 15.2 to 15.6

Why

GATE 2025 official key: 15.2 to 15.6m2.15.6 m². Q =(70/60)×4200×40≈196,000= (70/60) \times 4200 \times 40 \approx 196,000 W. Counter-flow LMTD = (45−40)/ln(45/40) ≈42.45°C.\approx 42.45°C. Area = Q/(U·LMTD) =196000/(300×42.45)≈15.4m2.= 196000/(300 \times 42.45) \approx 15.4 m².

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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