Film condensation mass flow rate

The total heat flow (Q) at the film surface is equal to the mass flow rate (W k) times the heat of condensation (AH). That is, the heat generated by condensation at the surface must be equal to the heat transported away by conduction and radiation for steady state to be achieved. In mathematical terms this results in the equation. 

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. 

Conservation of mass and conservation of energy are next considered. Consider the control volume shown in Fig. 11.8. Between x and x + dx, i.e., over the length of the control volume,j the mass flow rate in the film (D increases because vapor condenses at the rate amv on the film and is absorbed into it Applying conservation of mass to the control volume gives ... 

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. 

The mass flow rate of the condensate film follows as... 

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. 

In the framework of Nusselt s film condensation theory, using the mass flow rate for the condensate, eq. (4.9),... 

The mass flow rate of film condensate at any point x for unit depth is... 

The schematic diagram of the experimental setup is shown in Fig. 2 and the experimental conditions are shown in Table 2. Each gas was controlled its flow rate by a mass flow controller and supplied to the module at a pressure sli tly higher than the atmospheric pressure. Absorbent solution was suppUed to the module by a circulation pump. A small amount of absorbent solution, which did not permeate the membrane, overflowed and then it was introduced to the upper part of the permeate side. Permeation and returning liquid fell down to the reservoir and it was recycled to the feed side. The dry gas through condenser was discharged from the vacuum pump, and its flow rate was measured by a digital soap-film flow meter. The gas composition was determined by a gas chromatograph (Yanaco, GC-2800, column Porapak Q for CO2 and (N2+O2) analysis, and molecular sieve 5A for N2 and O2 analysis). The performance of the module was calculated by the same procedure reported in our previous paper [1]. 

Since the liquid is produced by condensation, the thickness of the film will be zero at the top and will gradually increase towards the bottom. Under stable conditions the difference in the mass rates of flow at distances x and x + dx from the top of the surface will result from condensation over the small element of the surface of length d r and width w, as shown in Figure 9.47. 

If G is the mass rate of flow of condensate, the mass rate of flow per unit area G is G/S and the Reynolds number for the condensate film is then given by ... 

In the previous discussion it has been assumed that the vapour is a pure material, such as steam or organic vapour. If it contains a proportion of non-condensable gas and is cooled below its dew point, a layer of condensate is formed on the surface with a mixture of non-condensable gas and vapour above it. The heat flow from the vapour to the surface then takes place in two ways. Firstly, sensible heat is passed to the surface because of the temperature difference. Secondly, since the concentration of vapour in the main stream is greater than that in the gas film at the condensate surface, vapour molecules diffuse to the surface and condense there, giving up their latent heat. The actual rate of condensation is then determined by the combination of these two effects, and its calculation requires a knowledge of mass transfer by diffusion, as discussed in Chapter 10. 

Remarks For tubular pipe, kf is the thermal conductivity of fluid at mean film temperature p/ is the fluid density at mean film temperature and Df are the outside and inside diameters of the tube is the viscosity of fluid at bulk fluid temperature m is the mass condensed per unit time f is the mass rate of condensate flow per unit perimeter of tube (kg/s m). The thickness for the condensate in Eqs. (5.11) and (5.12) for Re <2100 is given by /oond ( P-T/pj g) , where g is the gravitational constant. Smooth pipe surfaces are assumed in the relationships of Table 5.2. 

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