Chapter 11, Problem 11.1P

In a fire-tube boiler, hot products of combustion flowing through an array of thin-walled tubes are used toboil water flowing over the tubes. At the time of installation, the overall heat transfer coefficient was $400{\text{ W/m}}^2\cdot \text{K}$ . After 1 year of use, the inner and outertube surfaces are fouled, with cot-responding foulingfactors of $R_{f,i}^n=0.0015$ and $R_{f,o}^n=0.0005{\text{ m}}^2\cdot \text{K/W}$ ,respectively. Should the boiler be scheduled for cleaning of the tube surfaces?

To determine

Whether the boiler should be scheduled for cleaning of the tube surfaces.

Answer to Problem 11.1P

Scheduled cleaning is essential.

Explanation of Solution

Given information:

The overall heat transfer coefficient at the time of installation: $U=400W/m^2.K$

Fouling factors of inner and outer tube surfaces after 1 year of use:

  $\begin{array}{l}{R}_{f,i}^{"}=0.0015m^2.K/W\\ R_{f,o}^{"}=0.0005m^2.K/W\end{array}$

Calculations:

  

The overall heat transfer coefficient after one year is calculated as:

  $\begin{array}{l}\frac{1}{U}=\frac{1}{h_i}+\frac{1}{h_O}+R_{f,i}^{\text{'}\text{'}}+R_{f,o}^{\text{'}\text{'}}.\\ \sin ce,\\ \frac{1}{h_i}+\frac{1}{h_O}=\frac{1}{400W\text{/}{m}^2\cdot K}\end{array}$

  $\begin{array}{l}\frac{1}{U}=\frac{1}{400W\text{/}{m}^2\cdot K}+\left(0.0015+0.0005\right)m^2\cdot K\text{/}W=0.0045m^2\cdot K\text{/}W\\ U=222W\text{/}{m}^2\cdot K\end{array}$

Thus, periodic cleaning is essential for efficient boiler operation.

Conclusion: The boiler should be scheduled for cleaning of the tube surfaces