Question

Consider film condensation on the outer surfaces of four long tubes. For which orientation of the tubes will the condensation heat transfer coefficient be the highest: \((a)\) vertical, \((b)\) horizontal side by side, \((c)\) horizontal but in a vertical tier (directly on top of each other), or \((d)\) a horizontal stack of two tubes high and two tubes wide?

Short answer

Answer: The highest condensation heat transfer coefficient will be achieved for the vertical orientation (a) of the tubes.

Step-by-step solution

Plan of Action

The plan of action should involve evaluating the heat transfer coefficient for each orientation based on the effect of gravity on condensate draining and thermal state of the outer surface. The orientation that results in the maximum heat transfer coefficient will be selected as the answer.

Orientation (a): Vertical

In the vertical orientation, the tubes are aligned vertically. This allows gravity to assist in condensate drainage, leading to a thinner condensate film on the tube surfaces. A thinner condensate film means reduced thermal resistance and thus a higher heat transfer coefficient. Moreover, the tube surfaces have a uniform temperature throughout.

Orientation (b): Horizontal Side by Side

For horizontal side by side orientation, the tubes are placed horizontally and parallel to each other. The condensate accumulates at the bottom of the tube surface due to gravity and must flow along the circumference of the tubes. This creates a non-uniform temperature distribution along the tube surface, leading to a reduction in heat transfer coefficient as compared to the vertical orientation.

Orientation (c): Horizontal in a Vertical Tier

In this orientation, the tubes are horizontally placed but in a vertical tier (directly on top of each other). The condensate from the upper tubes tends to flow downwards and accumulate on the lower tubes, leading to a thicker film of condensate on the bottom tubes. This increases the thermal resistance and lowers the heat transfer coefficient compared to the vertical orientation.

Orientation (d): Horizontal Stack of Two Tubes High and Two Tubes Wide

In this configuration, there are a total of four tubes, two tubes on top of each other and two tubes side by side. This makes it difficult for the condensate drainage due to the interference caused by adjacent tubes. The increased condensate thickness on tubes and the non-uniform temperature distribution lead to lower heat transfer coefficients, as compared to the vertical orientation.

Conclusion

Comparing the four orientations, it is found that in the vertical orientation (a), gravity aids condensate drainage and results in a uniform temperature distribution on the tube surface, both factors leading to higher heat transfer coefficients. Therefore, the highest condensation heat transfer coefficient will be achieved for \((a)\) vertical orientation of the tubes.