Question

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$^{-1}$.
 

• A. 100
• B. 150
• C. 200
• D. 250

Hint:

When fouling occurs, add fouling resistance to the clean thermal resistance before taking the reciprocal to find the dirty heat transfer coefficient.

Answer 1

The Correct Option is C

The clean overall heat transfer coefficient is given as:
\[ U_{\text{clean}} = 250 \; \text{W m}^{-2} \text{K}^{-1}. \]

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.