Film coefficients condensing vapors

Film-type condensation is more common and more dependable. Dropwise condensation normally needs to be promoted by introducing an impurity into the vapor stream. Substantially higher (6 to 18 times) coefficients are obtained for dropwise condensation of steam, but design methods are not available. Therefore, the development of equations for condensation will be for the film type only. 

The physical properties of the liquid, rather than those of the vapor, are used For determining the film coefficient for condensation. Nus-selt [2. Ver. Dt.sch. Ing., 60, 541, 569 (1916)] derived theoretical relationships for predicting the film coefficient of heat transfer for condensation of a pure saturated vapor. A number of simplifying assumptions were used in the derivation. 

Dukler Theory The preceding expressions for condensation are based on the classical Nusselt theoiy. It is generally known and conceded that the film coefficients for steam and organic vapors calculated by the Nusselt theory are conservatively low. Dukler [Chem. Eng. Prog., 55, 62 (1959)] developed equations for velocity and temperature distribution in thin films on vertical walls based on expressions of Deissler (NACA Tech. Notes 2129, 1950 2138, 1952 3145, 1959) for the eddy viscosity and thermal conductivity near the solid boundaiy. According to the Dukler theoiy, three fixed factors must be known to estabhsh the value of the average film coefficient the terminal Reynolds number, the Prandtl number of the condensed phase, and a dimensionless group defined as follows ... 

FIG. 5-9 Chart for determining film coefficient for film-type condensation of pure vapor, based on Eqs. 5-88 and 5-93. For vertical tubes multiply by 1.2. If 4F/ J exceeds 2100, use Fig. 5-10. is in U.S. customary units to convert feet to... 

Pressure can also be controlled by variable heat transfer coefficient in the condenser. In this type of control, the condenser must have excess surface. This excess surface becomes part of the control system. One example of this is a total condenser with the accumulator running full and the level up in the condenser. If the pressure is too high, the level is lowered to provide additional cooling, and vice versa. This works on the principle of a slow moving liquid film having poorer heat transfer than a condensing vapor film. Sometimes it is necessary to put a partially flooded condenser at a steep angle rather than horizontal for proper control response. 

Often, a reasonable and convenient way to understand the heat transfer process in a heat exchanger unit is to break down the types of heat transfer that must occur such as, vapor subcooling to dew point, condensation, and liquid subcooling. Each of these demands heat transfer of a different type, using different AT values, film coefficients, and fouling factors. This is illustrated in Figure 10-36. It is possible to properly determine a weighted overall temperature... 

Film-type condensation is considered to be the usual condition for most pure vapors, although drop-type condensation gives transfer coefficients many times larger when it does occur. For practical purposes, film-type is considered in design. 

The effect of a noncondensable gas in the system with a condensable vapor is to significandy reduce the condensing side film coefficient. Henderson and Marcello present data to illustrate the effect. Figures 10-85, 10-86, and 10-86A present the effect of AT with a steam-air system and toluene-... 

To calculate the outside film coefficient, you need to know the difference in temperature of the condensing vapor (T, ) and the pipe wall temperature (L). The pipe wall temperature is determined hy trial-and-error calculations using the following equation/ ... 

Example 15.4 A reboiler is required to supply 0.1 krnol-s 1 of vapor to a distillation column. The column bottom product is almost pure butane. The column operates with a pressure at the bottom of the column of 19.25 bar. At this pressure, the butane vaporizes at a temperature of 112°C. The vaporization can be assumed to be essentially isothermal and is to be carried out using steam with a condensing temperature of 140°C. The heat of vaporization for butane is 233,000 Jkg, its critical pressure 38 bar, critical temperature 425.2 K and molar mass 58 kg krnol Steel tubes with 30 mm outside diameter, 2 mm wall thickness and length 3.95 m are to be used. The thermal conductivity of the tube wall can be taken to be 45 W-m 1-K 1. The film coefficient (including fouling) for the condensing steam can be assumed to be 5700 W m 2-K 1. Estimate the heat transfer area for... 

Related Calculations. For most cases, vapor-shear condensation is not important, and the condensing heat-transfer coefficient can be calculated simply as the laminar-film coefficient. 

The process is described by the following sequence. The vapor diffuses to the boundary where actual condensation takes place. In most cases, the condensate forms a continuous layer over the cooling surface, draining under the influence of gravity. This is known as film condensation. The latent heat liberated is transferred through the film to the surface by conduction. Although this film offers considerable resistance to heat flow, film coefficients are usually high. 

If a mixture of condensable and noncondensable gases is cooled below its dew point at a surface, the former condenses, leaving the adjacent layers richer in the latter, thus creating an added thermal resistance. The condensable fraction must diffuse through this layer to reach the film of condensate and heat-transfer coefficients are normally very much lower than the corresponding value for the pure vapor. For example, the presence of 0.5% of air has been found to reduce the heat transfer by condensation of steam by as much as 50%. 

Figure 12.45 can be used to estimate condensate film coefficients in the absence of appreciable vapor shear. Horizontal and downward vertical vapor flow will increase the rate of heat transfer, and the use of Figure 12.45 will give conservative values for most practical condenser designs. 

Two flow models are used to estimate the mean condensation coefficient in horizontal tubes stratified flow, as in Figure 12.47a, and annular flow, as in Figure 12.47b. The stratified flow model represents the limiting condition at low condensate and vapor rates and the annular model, the condition at high vapor and low condensate rates. For the stratified flow model, the condensate film coefficient can be estimated from the Nusselt equation, applying a suitable correction for the reduction in the coefficient caused by the accumulation of condensate in the bottom of the tube. The correction factor will typically be around 0.8, so the coefficient for stratified flow can be estimated from... 

Approximate methods. The local coefficient for heat transfer can be expressed in terms of the local condensate film coefficient and the local coefficient for sensible-heat transfer from the vapor (the gas film coefficient) h, by a relationship first proposed by Silver (1947) ... 

U is the overall heat-transfer coefficient between the vapor-liquid interface and the coolant, including condensate film, dirt and wall resistances, and coolant. The condensate film coefficient is calculated from the appropriate equation or correlation for pure vapor condensation for the geometry and flow regime involved, using mean hquid properties. Zy is the ratio of the sensible heat removed from the... 

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