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GATE 2021 CH – Question 18

Heat Transfer · Heat exchangers and evaporators: types and design · 1 mark · Multiple choice

For a shell-and-tube heat exchanger, the clean overall heat transfer coefficient is calculated as $250\ \mathrm{W\,m^{-2}\,K^{-1}}$ for a specific process condition. It is expected that the heat exchanger may be fouled during the operation, and a fouling resistance of $0.001\ \mathrm{m^2\,K\,W^{-1}}$ is prescribed. The dirt overall heat transfer coefficient is _____ $\mathrm{W\,m^{-2}\,K^{-1}}$.

  1. 100
  2. 150
  3. 200
  4. 250

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Correct answer: (C) 200

Explanation

Fouling adds a resistance **in series** with the clean exchanger resistance:
$$\frac1{U_d}=\frac1{U_c}+R_f=\frac1{250}+0.001=0.005\ \mathrm{m^2K/W}.$$

Hence $U_d=1/0.005=\mathbf{200\ \mathrm{W\,m^{-2}K^{-1}}}$, **C**. The decrease from 250 is physically consistent with the added resistance.