For a shell-and-tube heat exchanger, the clean overall heat transfer coefficient is calculated as 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 a fouling resistance of 0.001 m$^{2}$ K W$^{-1}$ is prescribed. The dirt overall heat transfer coefficient is \(\underline{\hspace{2cm}}\) W m$^{-2}$ K$^{-1}$.
For a shell-and-tube heat exchanger, the clean overall heat transfer coefficient is calculated as 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 a fouling resistance of 0.001 m$^{2}$ K W$^{-1}$ is prescribed. The dirt overall heat transfer coefficient is \(\underline{\hspace{2cm}}\) W m$^{-2}$ K$^{-1}$.
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- 100
- 150
- 200
- 250
The Correct Option is C
Solution and Explanation
\[ U_{\text{clean}} = 250 \; \text{W m}^{-2} \text{K}^{-1}. \]
Step 1: Compute clean thermal resistance.
\[
\frac{1}{U_{\text{clean}}} = \frac{1}{250} = 0.004 \; \text{m}^2 \text{K W}^{-1}.
\]
Step 2: Add fouling resistance.
Fouling resistance = 0.001 m$^2$ K W$^{-1}$.
\[
R_{\text{total}} = 0.004 + 0.001 = 0.005.
\]
Step 3: Compute dirty overall heat transfer coefficient.
\[
U_{\text{dirty}} = \frac{1}{R_{\text{total}}}
= \frac{1}{0.005}
= 200 \; \text{W m}^{-2} \text{K}^{-1}.
\]
Thus, the dirt overall heat transfer coefficient is 200 W m⁻² K⁻¹.
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