Film Condensation on a Vertical Plate

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]

Film condensation on a vertical plate may be analyzed in a manner first proposed by Nusselt [I], Consider the coordinate system shown in Fig. 9-2. The plate temperature is maintained at 7 ,. and the vapor temperature at the edge of the him is the saturation temperature TK. The him thickness is represented by <5, and we choose the coordinate system with the positive direction of. v measured downward, as shown. It is assumed that the viscous shear of the vapor on the him is negligible at y -- 8. It is further assumed that a linear temperature distribution exists between wall and vapor conditions. The weight of the fluid element of thickness dx between y and 8 is balanced by the viscous-shear force at y and the buoyancy force due to the displaced vapor. Thus... 

We now consider film condensation on a vertical plate, as shown in Fig. 10 21. I he liquid film starts fornring at the top of the plate and flows downward under the influence of gravity, The thickness of the film S increases in the flow direction x because of continued condensation at the liquid-vapor interface. Heat in the amount hf (the latent heat of vaporization) is released during condensation and is transferred through the film to the plate surface at temperature 7j, Note that must be below tlie saturation temperature of the vapor for condensation to occur. 

Flow regime.s during film condensation on a vertical plate. 

The analytical relation for the heat transfer coefficient in film condensation on a vertical plate described above was first developed by Nusseli in 1916 under the following simplifying assumptions ... 

Using some simplifying assumptions, the average heat transfer coefiicient for film condensation on a vertical plate of height L is determined to be... 

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

Laminar Free Convection. Sparrow and Gregg [33] were the first to use the boundary layer method to study laminar, gravity-driven film condensation on a vertical plate. They improved upon the approximate analysis of Nusselt by including fluid acceleration and energy convection terms in the momentum and energy equations, respectively. Their numerical results can be expressed as ... 

H. Uehara, E. Kinosita, and S. Matsuda, Theoretical Study on Turbulent Film Condensation on a Vertical Plate, Proc. ASMEIJSME Thermal Eng. Conf, Maui, 2, pp. 391-397,1995. 

Figure 4.8-3. Film condensation on a vertical plate a) increase in film thickness with position, b) balance on element of condensate.

Mori, Y, K. Hiyikata, and K Utsunomiya, The Effect of Noncondensable Gas on Film Condensation Along a Vertical Plate in an Enclosed Chamber, ASME Journal Heat Trans., V. 99, May (1977) p. 257. 

O. A. Plumb, D. B. Burnett, and A. Shekarriz, Film Condensation on a Vertical Flat Plate in a Packed Bed, ASMEJ. Heat Transfer, (112) 235-239,1990. 

Laminar Free Convection. When a stagnant vapor condenses on a vertical plate, the motion of the condensate will be governed by body forces, and it will be laminar over the upper part of the plate where the condensate film is very thin. In this region, the heat transfer coefficient can be readily derived following the classical approximate method of Nusselt [12], Consider the situation depicted in Fig. 14.4 where the vapor is at a saturation temperature Ts and the plate surface temperature is T . Neglecting momentum effects in the condensate film, a force balance in the z-direction on a differential element in the film yields... 

Vertical Flat Plates. Following the earlier work by Bromley [190] on cylinders (see below), Hsu and Westwater [191] derived an expression for laminar film boiling on a vertical plate that is analogous to that for laminar film condensation. The average value of hc over a plate of height L is given by... 

Kinoshita, E, and Uehera, H., Turbulent Film Condensation of Binary Mixture on a Vertical Plate, ASME/JSME Thermal Engineering Conf., Vol. 2, pp367-373, 1995. 

The situation shown in Fig. 11.5 s considered here, i.e., consideration is given to film condensation on a cold isothermal vertical plate, held at temperature 7, which is exposed to a reservoir of saturated vapor at saturation temperature, Ts. 

The rate of condensation on a vertical surface is controlled by the force of gravity acting on the condensed liquid film. A consideration of Eq. (11.20) shows for example that for a vertical plate the mean heat transfer rate from the plate with laminar flow in the film is proportional to gw. Attempts have therefore been made to increase condensation rates by using centrifugal forces instead of the gravitational force to drain the condensed liquid film from the cold surface [55], The simplest example of this would be condensation on the upper surface of a cooled circular plate rotating in a horizontal plane. This situation is shown in Fig. 11.23. A Nusselt-type analysis of this situation will be considered in the present section. 

Stagnant saturated steam at 95°C condenses onto a vertical plate with a surface temperature of 90°C. The plate is 0.6 m high and 1.5 m wide. Determine whether the flow in the condensed liquid film remains laminar and then find the rate of condensation on the plate. 

When a saturated vapor condenses on a vertical, i.sothermal flat plate in a continuous film, the rale of heat transfer is proportional to... 

Example 4.1 Saturated steam at a pressure 9.8 10 3 MPa, condenses on a vertical wall. The wall temperature is 5 K below the saturation temperature. Calculate the following quantities at a distance of H = 0.08 m from the upper edge of the wall the film thickness 5(H), the mean velocity wm of the downward flowing condensate, its mass flow rate M/b per m plate width, the local and the mean heat transfer coefficients. 

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). 

Film thidcness S is typically two or three orders of magnitude smaller than the tube diameter it can therefore be found, for flow either inside or outside a tube, from the equation for a flat plate, Eq. (5.77). Since there is a temperature gradient in the film, the properties of the liquid are evaluated at the average film temperature 7., given by Eq. (13.11). For condensation on a vertical surface, for which cos) = 1, Eq. (5.77) becomes... 

Velkoff and Miller [336] investigated the effect of uniform and nonuniform electric fields on laminar film condensation of Freon-113 on a vertical plate. With screen grid electrodes providing a uniform electric field over the entire plate surface, a 150 percent increase in the heat transfer coefficient was obtained with a power expenditure of a fraction of one watt. Choi and Reynolds [337] and Choi [338] recently reported data for condensation of Freon-113 on the outside wall of an annulus in the presence of a radial electric field. With the maximum applied voltage of 30 kV, the average heat transfer coefficients for a 25.4-mm outside diameter by 12.7-mm inside diameter annulus were increased by 100 percent. 

Flow regimes in a condensed film on a vertical fiat plate. 

Stagnant saturated steam at 80°C condenses on a 0 -m high vertical plate with a surface temperature of 75°C. Calculate the heat transfer rate and condensation rate per meter u idth of the plate assuming that the flow in the liquid film is steads and laminar. Also find the maximum film thickness. 

Consider a vertical plate of height L and width b maintained at a constant temperature r, that is exposed to vapor at the saturation temperature The downward direction is taken as the positive x-direction with the origin placed at the lop of the plate whete condensation initiates, as shown in Fig. 10-24. The surface temperature is below the saluratioii temperature (7 j < r <) and thus the vapor condenses on the surface. The liquid film flows downward under the influence of gravity. The film thickness S and thus the mass flow rate of the Condensate increases with x as a result of continued condensation on the existing film. Then heal transfer from the vapor to the plate must occur through the film, which offers resistance to heat transfer. Obviously the thicker the film, ihe larger its thermal resistance and thus the lower the rate of heal transfer. 

Laminar film condensation on vertical or inclined plates, and on the inside or outside of a vertical tube. 

Shang and Adamek [15] recently studied laminar film condensation of saturated steam on a vertical flat plate using variable thermophysical properties and found that the Nusselt theory with the Drew [14] reference temperature cited above produces a heat transfer coefficient that is as much as 5.1 percent lower than their more correct model predicts (i.e., the Nusselt theory is conservative). 

D. Y. Shang and T. Adamek, Study on Laminar Film Condensation of Saturated Steam on a Vertical Flat Plate for Consideration of Various Physical Factors Including Variable Thermophysical Properties, Wdrme-und Stoffiibertragung, 30, pp. 89-100,1994. 

Wet electrostatic precipitators (WESP) are used for removal of liquid contaminants such as sulfuric acid mist, aerosols, and particulate matter. The acid mist and aerosols are typically formed in a WGS by condensation of SO3. Unlike dry precipitators, wet precipitators do not require rapping to remove the dust. The collected mist and particulate matter form a liquid film that runs down a vertical collecting plate. In some cases, a continuous spray of liquid is used to prevent solids deposition on the collecting plates. 

It should be noted that the x-coordinate is measured vertically downward along the plate surface and the y-coordinate is measured perpendicular to the plate surface. For condensation to occur, the wall temperature, Tw, must be lower than the saturation temperature, Ts, corresponding to the vapor reservoir pressure. Vapor condenses on the plate forming a thin film of liquid that flows down the plate under the influence of gravity. The thickness of the film, 5, and the local mass flow rate increase with distance down the plate as condensate forms continuously along the entire film/vapor interface. 

The basic Nusselt analysis ignores inertial effects in the condensed film and subcooling effects. Approximate methods of accounting for subcooling were discussed above. A method of accounting for both effects is discussed in this section. To illustrate the method, condensation on an isothermal vertical plate is again considered [52] to [54]. Interfacial shear stress effects will be neglected. 

Consider a vertical flat plate exposed to a condensable vapor. If the temperature of the plate is below the saturation temperature of the vapor, condensate will form on the surface and under the action of gravity will flow down the plate. If the liquid wets the surface, a smooth film is formed, and the process is called film condensation. If the liquid does not wet the surface, droplets are formed which fall down the surface in some random fashion. This process is called dropwise condensation. In the film-condensation process the surface is blanketed by the film, which grows in thickness as it moves down the plate. A temperature gradient exists in the film, and the film represents a thermal resistance to heat transfer. In dropwise condensation a large portion of the area... 

At a distance x down a vertical, isothermal flat plate on which a saturated vapor is condensing in a continuous film, the thickness of the liquid condensate layer is 8. The heal transfer coefficient at this location on the plate is given by (a) kJS (b) Shf (c) Sh ... 

Labunzov, D.A. Heat transfer in film condensation of pure vapours on vertical plates and horizontal tubes (russ.). Teploenergetika 7 (1957) 72-79... 

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