Vapor shear stress

When the vapor shear stress on the liquid film is accounted for, the heat transfer rate is given by ... 

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. 

FIGURE 14.7 Effect of turbulence and vapor shear stress during film condensation on a vertical plate [21],... 

During shell-side condensation in tube bundles, neighboring tubes disturb the vapor flow field and create condensate that flows from one tube to another under the action of gravity and/or vapor shear stress forces. The effects of local vapor velocity and condensate inundation must, therefore, be properly accounted for when calculating the average heat transfer in the bundle. Marto and Nunn [53], Marto [54], and Fujii [55] provide details of these phenomena. 

Rheology. The rheology of foam is striking it simultaneously shares the hallmark rheological properties of soHds, Hquids, and gases. Like an ordinary soHd, foams have a finite shear modulus and respond elastically to a small shear stress. However, if the appHed stress is increased beyond the yield stress, the foam flows like a viscous Hquid. In addition, because they contain a large volume fraction of gas, foams are quite compressible, like gases. Thus foams defy classification as soHd, Hquid, or vapor, and their mechanical response to external forces can be very complex. 

T Solid-vapor interfacial energy dyn/cm dyn/cm z Pow der shear stress kg/cm psf... 

Dynamic viscosity Kinematic viscosity Density Surface tension Shear stress Vapor quality Contact angle Shear viscosity Shear rate... 

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]

When a co-current vapor flow is present, the basic nature of this flow does not change, but the details differ because of the thinning of the liquid film by interfacial shear stress. Dropping the convective terms we can write the Navier-Stokes equations for steady film flow as follows ... 

A model of deformed evaporating liquid film, which is moved hy co-current vapor flow and gravity, is developed. Shear stress from co-current vapor is included as a boundary condition on interface. Intermolecular forces are taking into account as disjoining pressure component and surface roughness is considered also. 

At a shear stress close to the breaking point, or 7 kg force per cm2, -j,g creep rate was about 10 " cm mln i at V -10°C. If the boundary region is taken to be of about the thickness of the vapor adsorbed film, Xq = lOA, Equation 9 yields an effective boundary region viscosity of 6x10 poise. This value, while... 

Laminar Forced Convection. When the vapor moves in relation to the condensate, a shear stress xg will develop at the liquid-vapor interface. At very high vapor velocities, this shear... 

In real situations, the vapor velocity varies with position along the plate, and the interfacial shear stress is not constant since mass is removed due to condensation. The variation in vapor velocity depends upon the condensation rate and any changes in the vapor cross sectional flow area. For moderate condensation rates, the interfacial shear stress may be approximated by ... 

Rohsenow et al. [21] extended the analysis into the turbulent film regime using the heat transfer-momentum analogy. The results for a downward flowing vapor are shown in Fig. 14.7 for Prf = 1.0 and 10.0. At high vapor velocities, as the dimensionless shear stress x increases, the transition to turbulence occurs at smaller values of the film Reynolds number (Eq. 14.31) as represented by the dashed lines. The influence of x on both laminar and turbulent film condensation is evident. 

For practical values of H and Prf, Eq. 14.33 was found to be near unity, indicating that acceleration and convection effects are negligible. Chen [34] included the effect of vapor drag on the condensate motion by using an approximate expression for the interfacial shear stress. He was able to neglect the vapor boundary layer in the process and obtained the results shown in Fig. 14.8. The influence of interfacial shear stress is negligible at Prandtl numbers of ordinary liquids (nonliquid metals, Pr< > 1). Chen [34] was able to represent his numerical results by the approximate (within 1 percent) expression ... 

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