Thickness condensate film

The Reynolds number of the condensate film (falling film) is 4r/ I, where F is the weight rate of flow (loading rate) of condensate per unit perimeter kg/(s m) [lb/(h ft)]. The thickness of the condensate film for Reynolds number less than 2100 is (SflF/p g). ... 

With tube side condensation, coefficients are generally lower than for comparable shell side condensers. This phenomenon is attributed to (1) lower coolant velocities outside the tubes than are possible with tube side cooling, and (2) increased film thicknesses, namely, film resistance inside the tubes. 

Whereas a film formed in dry air consists essentially of an anhydrous oxide and may reach a thickness of 3 nm, in the presence of water (ranging from condensed films deposited from humid atmospheres to bulk aqueous phases) further thickening occurs as partial hydration increases the electron tunnelling conductivity. Other components in contaminated atmospheres may become incorporated (e.g. HjS, SO2, CO2, Cl ), as described in Sections 2.2 and3.1. 

Benzene vapour, at atmospheric pressure, condenses on a plane surface 2 m long and I m wide, maintained at 300 K and inclined at an angle of 45° to the horizontal. Plot the thickness of the condensate film and the point heat transfer coefficient against distance from the top of the surface. 

The most useful type of standard state is one defined in terms of a small number of molecules per unit area of adsorbent surface. In an attempt to have a definition analogous to that for three-dimensional matter—one atmosphere at any temperature—Kemball and Rideal (12) defined a standard state with an area per molecule of 22.53T A.2 where T is the absolute temperature. This corresponds to the same volume per molecule as the three-dimensional state if the thickness of the surface layer is 6A. In terms of surface pressure it corresponds to 0.0608 dynes/cm. for a perfect two-dimensional gas at all temperatures, and as such the definition may be extended to cover condensed films. 

In the following derivation we will assume an almost complete wetting of the substrate by the material, in such a way that a continuous amorphous condensed film is formed at a thickness h smaller than the critical size of nucleation. In order to evaluate dG/dN of the process of incorporation of molecules from the amorphous condensed film to the spherulite, that is the ordered phase, we will hypothesize that the thickness of the amorphous film increases linearly with time, h(t) = Uhf, where the velocity is a constant, and that the spherulite has a cylindrical shape of radius R and height h, as illustrated in Fig. 5.10. 

Straight chain saturated hydrocarbon molecules from propane (C3H8) to octane (CgHis) were deposited from the vapor phase on platinum and silver(l 11) crystal surfaces in the temperature range 100—200 K. The ordered monolayer was produced first and then, with decreasing temperature a thick crystalline film was condensed and the surface structures of these organic crystals were also studied by LEED ... 

With cryosurfaces, it is convenient to reduce e as much as possible by polishing or gold-plating (s 0.03). The accumulation of condensate changes s considerably, however, and, for condensate films a few millimetres thick, it can increase significantly and approach 0.9 (s for a black body =1). 

It should be noted that the Eqs. (11.19) and (11.21) are also valid for condensation on the outside surface of vertical tubes [44], provided the radius of the tube is large compared to the film thickness as indicated in Fig. 11.9. Since condensate films are typically very thin in practical situations, this condition is usually met. 

Summary of the properties of molecules as learned from surface films. The study of condensed films has shown that the molecules of long-chain compounds are elongated objects, several times as long as thick that they orient themselves very steeply to the surface, and that their end groups are often different in shape and size from the CH2 groups in the chains, sometimes forming projections on the ends of the chains. 

The carbon dioxide leading tube was configured in such a way, that the thickness of the condensate film at the outside of this tube does not influence the heat transfer measurements, regardless of the angle of inclination. For that purpose the tube has been finned on the outside. The geometry of those fins as well as the distances between them have been chosen in such a way, that the temperature differences on the outer wall along the tube never exceed 0.5°C, regardless of the inclination of the tube. 

A general formula for calculation of the dispersion molecular interactions in any type of condensed phases has been proposed in [148], The attraction between bodies results from the existence of fluctuational electromagnetic field of the substance. If this field is known in a thin film, then it is possible to determine the disjoining pressure in it. The more strict macroscopic theory avoids the approximations assumed in the microscopic theory, i.e. additivity of forces integration extrapolation of interactions of individual molecules in the gas to interactions in condensed phase. The following function for IIvw was derived in [148] for thick free films... 

The evaluation of the hydraulic diameter Df, for some common geometries is illustrated iri Fig. 10-22. Note that the hydraulic diameter is again defined such that it reduces to (he ordinary diameter for flow in a circular lube, as was done in Chapter 8 for internal flow, and it is equivalent to 4 times the thickness of the condensate film at the location where the hydraulic diameter is evaluated. That i5, D — 4S. 

To investigate the elastic properties resulting from ether-functionalized silylester condensates, the diethoxymethyl derivatives were used in 1 1-mixtures with the commercial stone consolidant F510 of Remmers Bauchemie to prepare thick siloxane films in Petri dishes. Fig. lb shows a photograph of the polycondensate obtained from F510 modified with (3-methoxypropyl)diethoxymethylsilane. In comparison with the film produced by hydrolysis and condensation of the unmodified consolidant (Fig. la), considerably less shrinking fissures are observed. 

For a vertical condensing liquid film, scale analysis of the 2-dimensional constant-property conservation equations of mass, momentum and energy, with appropriate boundary conditions, shows that Rafii is a measure of the slenderness ratio L/d of the film (18). Here L is taken as the streamwise length of the condensation film and d an average film thickness. This interpretation is valid in the limit where the momentum equation is a balance of viscous and gravitational forces. Under such conditions, a velocity scale is... 

As Fig. 4.6 shows, saturated steam at a temperature s is condensing on a vertical wall whose temperature 0 is constant and lower than the saturation temperature. A continuous condensate film develops which flows downwards under the influence of gravity, and has a thickness 5 x) that constantly increases. The velocity profile w(y), with w for wx, is obtained from a force balance. Under the assumption of steady flow, the force exerted by the shear stress are in equilibrium with the force of gravity, corresponding to the sketch on the right hand side of Fig. 4.6... 

As we can see from the equations given above, large heat transfer coefficients are achieved when the temperature difference 1 S — 1 0 and the height of the wall are small. In both cases the condensate film is thin and so the resistances to heat transfer are low. The results from above are also valid for condensation of vapours on the internal and external walls of vertical tubes, if the tube diameter is large in comparison to the film thickness. The width b = nd has to be inserted into (4.13a). 

It follows from this that, under the assumptions made, the specific enthalpy hi, of the flowing condensate is independent of the film thickness. The equation further shows that the enthalpy of vaporization Ahv in the equations for Nusselt s film condensation theory has to be replaced by the enthalpy difference Ah. If we additionally consider that the temperature profile in the condensate film is slightly curved, then according to Rohsenow [4.10] in place of (4.27), we obtain for Ah the more exact value... 

To be able to estimate the influence of the inert gas on the heat transfer we will consider a condensate film of thickness S. In front of this there is vapour with an inert gas. If there was no inert gas present, the surface of the film would be at the saturation temperature i9B(p) and the heat flux released would be... 

Nusselt s film condensation theory presumes a laminar film flow. As the amount of condensate increases downstream, the Reynolds number formed with the film thickness increases. The initially flat film becomes wavy and is eventually transformed from a laminar to a turbulent film the heat transfer is significantly better than in the laminar film. The heat transfer in turbulent film condensation was first calculated approximately by Grigull [4.14], who applied the Prandtl analogy for pipe flow to the turbulent condensate film. In addition to the quantities for laminar film condensation the Prandtl number appears as a new parameter. The results can not be represented explicitly. In order to obtain a clear representation, we will now define the Reynolds number of the condensate film... 

The Reynolds number Re = wm 6/z/L for the condensation on a vertical tube can, due to the mass balance M = wm dn 8 gL and with r/L = i/LgL, also be written as Re = M/(d,TT i]L ). As the tube diameter d, on which the calculations from Fig. 4.12 are based, is much larger than the assumed thickness of the film, the curvature of the condensate film has no effect on the heat transfer. The results also hold for condensation on a vertical flat plate, with the Reynolds number defined in (4.38). 

Note that Eq. (9.19) predicts that the actual pressure drop is two orders of magnitude larger than the gas pressure drop. Actually the capillary pressure works on the effective pore radius, which equals (r - f) with t the adsorbed condensate film thickness and which is assumed to be immobile this point is discussed below. A force balance for one end of the capillary with length L and radius r then yields the effective capillary pressure Pc,eif... 

On perfectly horizontal tubes a condensed film will increase its thickness towards the bottom of the tube (Fig. 15.2). Some of the condensed liquid will fall onto lower tubes, increasing the liquid load, and decreasing the heat transfer coefficient on those tubes. Even a slight inclination of the tube is sufficient to cause the condensate to drain in the direction of the slope. A horizontal shell and tube condenser is likely to be baffled so as to force the vapor to flow horizontally across the tubes. Other flow arrangements are, however, possible. 

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