Chemegate

GATE 2024 Chemical Engineering, Q38 · Heat Transfer

The correct answer is A, 17.9.

Question

Hot oil at 110°C110°C heats water from 30°C30°C to 70°C70°C in a counter-current double-pipe heat exchanger. The flow rates of water and oil are 50 kg/min and 100 kg/min, respectively, and their specific heat capacities are 4.2kJ/(kg°C)4.2 kJ/(kg\cdot °C) and 2.0kJ/(kg°C),2.0 kJ/(kg\cdot °C), respectively. Assume the heat exchanger is at steady state. If the overall heat transfer coefficient is 200W/(m2°C),200 W/(m²\cdot °C), the heat transfer area in m2 is

  • A. 17.9
  • B. 1.1
  • C. 5.2
  • D. 35.2

Official answer: 17.9

Why

GATE 2024 official key: (A). Q =(50/60)×4200×40140,000= (50/60) \times 4200 \times 40 \approx 140,000 W. Oil outlet: 140000=(100/60)×2000×(110Tout)Tout=68°C.140000 = (100/60) \times 2000 \times (110−T_{out}) \Rightarrow T_{out} = 68°C. LMTD (counter-current) = (40−38)/ln(40/38) 39.0°C.\approx 39.0°C. Area =140000/(200×39.0)17.9m2.= 140000/(200 \times 39.0) \approx 17.9 m².

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