Plates film condensation

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. 

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. 

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. 

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. 

Laminar film condensation on a rotating horizontal circular plate. 

Control volume used in the analysis of laminar film condensation on a rotating horizontal circular 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]

Chen. M.M., An Analytical Study of Laminar Film Condensation. Part 1. Flat Plates Part 2. Single and Multiple Horizontal Tubes." J. Heat Transfer, Vol. 83. pp. 48-60,1961. 

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... 

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... 

B Derive a relation for the heat transfer coefficient in laminar film condensation over a vertical plate,... 

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. 

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. 

Equation 10 22 for vertical plates can also be used to calculate the average heat transfer coefficient for laminar film condensation on the outer surfaces of vertical lubes provided that the tube diameter is large relative to the thickness of the liquid film. 

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

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

Chen, M.M. An analytical study of laminar film condensation. Part 1. Flat plates. Part 2. Single and multiple horizontal tubes. Trans. Am. Soc. Mech. Eng., Ser. C. J. Heat... 

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

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. 

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. 

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). 

FIGURE 14.5 Average heat transfer coefficients for film condensation on vertical plates. 

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 ... 

Nimmo and Leppert [111] used a Nusselt-type analysis to study laminar film condensation on a finite, upward-facing horizontal plate, assuming that the condensate flow was driven by the hydrostatic pressure gradient due to changes in condensate film thickness from the center of the plate to the edges. They arrived at the following approximate expression for the mean Nusselt number ... 

Chiou and Chang [113] analyzed laminar film condensation on a horizontal upward-facing disk and found that their model overpredicts the theoretical result from Eq. 14.98 by about 25 percent. They attribute this to the fact that on a disk, the surface area increases radially outward, and this makes the condensate film thinner than on a rectangular plate, as studied by Nimmo and Leppert [111]. 

For this case, the resulting time-dependent heat transfer coefficient is ke/S(t). Prasad and Jaluria [114] extended the above simple analysis to the situation where runoff over the plate edges is allowed by conducting a boundary layer analysis of transient film condensation on a horizontal plate. 

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. 

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. 

R. D. Cess, Laminar Film Condensation on a Flat Plate in the Absence of a Body Force, Z. Angew. Math. Phys., 11, pp. 426-433,1960. 

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