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GATE 2024 CH – Question 38

Heat Transfer · Heat exchangers and evaporators: types and design · 2 marks · Multiple choice

Hot oil at 110 °C heats water from 30 °C to 70 °C in a counter-current double-pipe heat exchanger. The flow rates of water and oil are 50 kg min$^{-1}$ and 100 kg min$^{-1}$, respectively and their specific heat capacities are 4.2 kJ kg$^{-1}$ °C$^{-1}$ and 2.0 kJ kg$^{-1}$ °C$^{-1}$, respectively. Assume the heat exchanger is at steady state. If the overall heat transfer coefficient is 200 W m$^{-2}$ °C$^{-1}$, the heat transfer area in m$^2$ is

  1. 17.9
  2. 1.1
  3. 5.2
  4. 35.2

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Correct answer: (A) 17.9

Explanation

The duty is $Q = 50 \times 4.2 \times 40 = 8400$ kJ/min $= 140$ kW. The oil outlet temperature is $110 - \frac{8400}{100 \times 2} = 68$ °C. For counter flow, $\Delta T_1 = 110 - 70 = 40$ °C and $\Delta T_2 = 68 - 30 = 38$ °C, so $\Delta T_{lm} = \frac{40 - 38}{\ln(40/38)} = 38.99$ °C. Then $A = \frac{140000}{200 \times 38.99} = 17.9$ m².