Deviations from Nusselts film condensation theory

3 Deviations from Nusselt s film condensation theory 

Experiments on film condensation of saturated vapour on vertical walls yield deviations by as much as +25% from the heat transfer coefficients according to Nusselt s film condensation theory. There are different reasons that are decisive for this. 

Nusselt s film condensation theory presumes an even increase in the thickness of the film due to further condensation. However experiments, among others [4.4] to [4.6], have shown that even in a flow that is clearly laminar, waves can develop at the film surface. These types of waves were not only observed on rough but also on polished surfaces. Obviously this means that the disturbances in the velocity that are always present in a stream are not damped under certain conditions, and so waves form. They lead to an improvement in the heat transfer of 10 to 25 % compared to the predictions from Nusselt s theory. According to Grimley [4.7], waves and ripples appear above a critical Reynolds number 

12) and (4.13) of Nusselt s film condensation theory the material properties of the condensate are presumed to be independent of temperature. This assumption is well met if the temperature drop ds — -do in the condensate film is sufficiently small. In any other case the change in the dynamic viscosity, the thermal conductivity, and on a lower scale the density of the condensate film with the temperature has to be considered. In place of (4.5) the momentum balance appears 

These equations are to be solved under the boundary conditions 

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Fig. 4.7 illustrates (4.24). As we can see from the graph, the temperature dependence of the dynamic viscosity and the thermal conductivity can have a marked influence on the heat transfer, as far as they change starkly with the temperature. In condensing steam, for a temperature difference between the saturation and wall temperatures of s — i o < 50 K, the material properties vary for As/Ao between 0.6 and 1.2 and for Vs/vo between 1 and 1.3. This region is hatched in Fig. 4.7. It is clear that within this region the deviations from Nusselt s film condensation theory are less than 3%.

A further, and likewise small, deviation from Nusselt s film condensation theory is found for superheated vapour. In addition to the enthalpy of vaporization, the superheat enthalpy CpQ ( g — < s) has to be removed in order to cool the superheated vapour from a temperature da to the saturation temperature t9s at the phase interface. Instead of the enthalpy difference Ahv according to (4.28), the enthalpy difference... 

If a deviation of 1 % from the values for Nusselt s film condensation theory is permitted, this leads to a Reynolds number of... 

If the wall is inclined at an angle 7 to the vertical then the acceleration due to gravity g has to be replaced by its component parallel to the wall g cos 7 with 0 < 7 < 7r/2. The equation also holds for condensation of quiescent vapours on the inside or outside of a vertical tube, if the diameter of the tube is large in comparison to the film thickness. The width b has to be replaced by b = ir d. If a deviation of 1 % from the values from Nusselt s film condensation theory is permitted, then the equation is valid up to a Reynolds number... 

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