Question

Consider film condensation on a vertical plate. Will the heat flux be higher at the top or at the bottom of the plate? Why?

Short answer

Answer: The heat flux is higher at the top of the vertical plate undergoing film condensation. This is because the condensate film is thinner at the top of the plate, resulting in less resistance to heat transfer compared to the bottom of the plate where the film is thicker due to the accumulation of condensate and gravitational force acting on the liquid.

Step-by-step solution

Understand Film Condensation

Film condensation occurs when a vapor comes in contact with a surface that is cooler than the vapor's saturation temperature. The vapor condenses into a liquid film on the surface, which then flows along the surface due to gravity. Heat transfer occurs through the liquid film, the effectiveness of which depends on the thickness and thermal properties of the film.

Discuss the Role of Gravity

In a vertical plate configuration, gravity has a significant impact on the behavior of the condensate film. As the film flows down the plate, its thickness increases due to the accumulation of condensate. This increase in thickness affects the heat transfer through the film, as the resistance to heat transfer is directly proportional to the thickness of the film.

Heat Flux and Condensate Film Thickness Relationship

The heat flux (q) can be calculated using the following equation: q = -k * (dT/dx) where k is the thermal conductivity of the condensate film, dT is the temperature difference between the surface and the bulk fluid, and dx is the thickness of the film. We can see from the equation that, as the thickness of the film (dx) increases, the heat flux (q) decreases.

Analyze Heat Flux Distribution Along the Plate

Considering the role of gravity in increasing the thickness of the condensate film as it flows down the vertical plate, it becomes apparent that the film will be thinner and offer less resistance to heat transfer at the top of the plate compared to the bottom. Therefore, the heat flux will be higher at the top of the plate.

Conclusion

In conclusion, the heat flux will be higher at the top of the vertical plate undergoing film condensation. This is because the condensate film is thinner at the top of the plate, resulting in less resistance to heat transfer compared to the bottom of the plate where the film is thicker due to the accumulation of condensate and gravitational force acting on the liquid.