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Chapter 10: Problem 56

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

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Step by step solution

01

Understanding Film Condensation

Film condensation occurs when a vapor cools and turns into a liquid, forming a thin film on a cold surface like a vertical plate. The heat is conducted through the liquid film to the cold surface. The heat flux depends on the film thickness and temperature difference between the film and the cold surface.
02

Effect of Gravity

Gravity plays a significant role in film condensation on a vertical plate. The liquid film flows downward due to gravitational force, causing the film to become thicker as it moves down the plate. This increase in thickness leads to a reduction in heat flux at the bottom of the plate as compared to the top.
03

Nusselt's Theory and Heat Flux

According to Nusselt's theory of film condensation, for laminar flow on a vertical plate, the film thickness (δ) is given by the equation: \[ \delta = \left( \frac{4 \nu_{L} x}{g \Delta T} \right)^{1/4} \] where: - \( \delta \) is the film thickness - \( \nu_{L} \) is the kinematic viscosity of the liquid - x is the distance from the top of the plate - g is the acceleration due to gravity - \( \Delta T \) is the temperature difference between the film and the cold surface Since the film thickness (δ) increases with x (distance from the top of the plate), the heat flux decreases as we move from the top to the bottom of the plate.
04

Conclusion

In conclusion, the heat flux will be higher at the top of the vertical plate compared to the bottom. This is because the liquid film becomes thicker as it moves downward due to gravity, and the thickness of the film plays a major role in determining the heat flux.

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Most popular questions from this chapter

A 65 -cm-long, 2-cm-diameter brass heating element is to be used to boil water at \(120^{\circ} \mathrm{C}\). If the surface temperature of the heating element is not to exceed \(125^{\circ} \mathrm{C}\), determine the highest rate of steam production in the boiler, in \(\mathrm{kg} / \mathrm{h}\).

What is the difference between film and dropwise condensation? Which is a more effective mechanism of heat transfer?

Saturated water vapor at \(40^{\circ} \mathrm{C}\) is to be condensed as it flows through a tube at a rate of \(0.2 \mathrm{~kg} / \mathrm{s}\). The condensate leaves the tube as a saturated liquid at \(40^{\circ} \mathrm{C}\). The rate of heat transfer from the tube is (a) \(34 \mathrm{~kJ} / \mathrm{s}\) (b) \(268 \mathrm{~kJ} / \mathrm{s}\) (c) \(453 \mathrm{~kJ} / \mathrm{s}\) (d) \(481 \mathrm{~kJ} / \mathrm{s}\) (e) \(515 \mathrm{~kJ} / \mathrm{s}\)

A long cylindrical stainless steel rod \(\left(c_{p}=\right.\) \(450 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}, \rho=7900 \mathrm{~kg} / \mathrm{m}^{3}, \varepsilon=0.30\) ) with mechanically polished surface is being conveyed through a water bath to be quenched. The \(25-\mathrm{mm}\)-diameter stainless steel rod has a temperature of \(700^{\circ} \mathrm{C}\) as it enters the water bath. \(\mathrm{A}\) length of \(3 \mathrm{~m}\) of the rod is submerged in water as it is conveyed through the water bath during the quenching process. As the stainless steel rod enters the water bath, boiling would occur at \(1 \mathrm{~atm}\). In order to prevent thermal burn on people handling the rod, it must exit the water bath at a temperature below \(45^{\circ} \mathrm{C}\). Determine the speed of the rod being conveyed through the water bath so that it leaves the water bath without the risk of thermal burn hazard.

Name the different boiling regimes in the order they occur in a vertical tube during flow boiling.
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