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

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