Film condensation surface shear stress

Vapor can condense on a cooled surface in two ways. Attention has mainly been given in this chapter to one of these modes of condensation, i.e.. to him condensation. The classical Nusselt-type analysis for film condensation with laminar film flow has been presented hnd the extension of this analysis to account for effects such as subcooling in the film and vapor shear stress at the outer edge of the film has been discussed. The conditions under which the flow in the film becomes turbulent have also been discussed. More advanced analysis of laminar film condensation based on the use of the boundary layer-type equations have been reviewed. 

Effect of Surface Shear Stress on Film Condensation on... 

Film condensation in tube bundles (more commonly used in shell-and-tube heat exchangers) characterize more complex physical conditions compared to condensation on a single tube. The gravity-controlled and surface-shear-stress-influenced condensate films must be modeled in different ways to accommodate combined influences of condensate drain to lower tubes (i.e., condensate inundation) and shear effects. Such a correlation, the fourth correlation from the top of Table 17.24, was proposed by Kern and modified by Butterworth [81]. 

R Shear stress at free surface of condensate film N/m2 ML- T 2... 

In the analysis of film condensation given in the previous sections it was assumed that the shear stress at the outer edge of the film was negligible. In some situations, however, particularly when the vapor velocity is high, this assumption may not be justified, i.e., the shear stress exerted on the outer surface of the condensed liquid film may have a significant influence on the heat transfer rate. The action of the shear stress on the surface of the liquid film is illustrated in Fig. 11.17. 

Consider laminar film condensation on a vertical plate when the vapor is flow ing parallel to the surface in a downward direction at velocity, V. Assume that a turbulent boundary layer is formed in the vapor along the outer surface of the laminar liquid film. Determine a criterion that will indicate when the effect of the shear stress at the outer edge of the condensed liquid film on the heat transfer rate is less than 59c. Assume that pv [Pg.602]

At the wall, y = 0, the velocity is w = 0, and if we further assume that the vapour velocity is not very large, and as a result of this that the shear stress exerted by the vapour on the condensate film is low, then at the surface of the condensate y = S... 

Nusselt extended his film condensation theory to take into account the influence of vapour flowing along the condensate film on the velocity of the condensate. The boundary conditions for (4.6) are no longer dw/dy = 0 for y = 6, instead the velocity profile ends with a finite gradient at the free surface of the film corresponding to the shear stress exerted by the flowing vapour. In (4.6) for the velocity profile... 

When vapor is moving at a large approaching velocity, the shear stress between the vapor and the condensate surface must be taken into account (i.e., shear forces are large compared to gravity force). A good review of the work devoted to this problem is found in Rose [85], who provided a detailed discussion of film condensation under forced convection. In Table 17.24, a correlation derived by Fuji et al. [86] and suggested by Butterworth [81] is included for the vapor shear effect. The same equation can be applied for a tube bundle. In such a situation, the approach velocity u should be calculated at the maximum free-flow area cross section within the bundle. 

Theoretical analysis of filmwise condensation of a stationary pure saturated vapor was originally presented by Nusselt (1916) for vertical surface (Figure 22.24). This analysis assumed laminar flow and constant properties for liquid film, no shear stress at the liquid-vapor interface, vapor at saturation temperature, and heat transfer through the film by conduction only. 

Nussdt himself derived the development of the film thickness and the heat transfer coefficient in case of laminar flow and neglected shear stress at the film surface [27]. Regarding a finite shear stress the film thickness of a condensating pure vapor phase at a distinct vertical position x reads as follows [42, 58] ... 

Shear force measurements between mica surfaces immersed in simple liquids such as cydohexane or OMCTS showed that as the two surfaces approach each other from a large separation, the confined liquids retain their bulk fluidity, across the entire gap, until at a critical spadng, which is characteristic of each liquid, the entire film undergoes an abrupt liquid-to-solid transition. This transition takes place because it becomes thermodynamically favorable to condense to a solid phase when confined to a thickness of 5-8 monolayers. Below the critical film thickness the films behave in a solid-like manner in the sense of requiring a critical lateral stress in order to shear them. On applying a shear force that exceeds the frictional force, the surfaces slide and their motion displays a characteristic stick-slip behavior, as shown schematically in the inset to Figure 1. 

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