Question

For a shell and tube heat exchanger, the clean overall heat transfer coefficient is calculated as 250 Wm\(^2\)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\(^2\)KW\(^{-1}\) is prescribed. The dirt overall heat transfer coefficient is ------------ Wm\(^2\)K\(^{-1}\).

• A. 300
• B. 200
• C. 100
• D. 50

Hint:

When considering fouling in heat exchangers, use the formula \( \frac{1}{U_{\text{dirty}}} = \frac{1}{U_{\text{clean}}} + R_{\text{fouling}} \) to calculate the dirty heat transfer coefficient.

Answer 1

The Correct Option is C

Step 1: Formula for overall heat transfer coefficient.
The overall heat transfer coefficient considering fouling is calculated by: \[ \frac{1}{U_{\text{dirty}}} = \frac{1}{U_{\text{clean}}} + R_{\text{fouling}} \] Where: - \( U_{\text{dirty}} \) is the overall heat transfer coefficient with fouling, - \( U_{\text{clean}} = 250 \, \text{Wm}^{-2}\text{K}^{-1} \) is the clean heat transfer coefficient, - \( R_{\text{fouling}} = 0.001 \, \text{m}^2\text{KW}^{-1} \) is the fouling resistance.

Step 2: Solve for the dirty heat transfer coefficient.
Substitute the known values into the equation: \[ \frac{1}{U_{\text{dirty}}} = \frac{1}{250} + 0.001 = 0.004 + 0.001 = 0.005 \] \[ U_{\text{dirty}} = \frac{1}{0.005} = 100 \, \text{Wm}^{-2}\text{K}^{-1} \]

Final Answer: \[ \boxed{100 \, \text{Wm}^{-2}\text{K}^{-1}} \]