Heat transfer from film condensation

Two cases are considered. The first, the laminar flow of a thin film down an inclined surface, is important in the heat transfer from a condensing vapour where the main resistance to transfer lies in the condensate film, as discussed in Chapter 9 (Section 9.6.1). The second is the flow in open channels which are frequently used for transporting liquids down a slope on an industrial site. 

Film-condensation coefficients for vertical surfaces. Film-type condensation on a vertical wall or tube can be analyzed analytically by assuming laminar flow of the condensate film down the wall. The film thickness is zero at the top of the wall or tube and increases in thickness as it flows downward because of condensation. Nusselt (HI, Wl) assumed that the heat transfer from the condensing vapor at 7, K, through this liquid film, and to the wall at 7 K was by conduction. Equating this heat transfer by conduction to that from condensation of the vapor, a final expression can be obtained for the average heat-transfer coefficient over the whole surface. 

Weak liquor will enter the plant and pass to the calandria where it will be drawn up as a thin film by the partial vacuum caused by ultimate condensation of vapour in the condenser. Vaporisation will take place due to heat transfer from condensing ammonia in the calandria, and the vapour and concentrated liquor will then pass to a separator from which the concentrated liquor will be... 

Heat-transfer coefficient in condensation Mean condensation heat-transfer coefficient for a single tube Heat-transfer coefficient for condensation on a horizontal tube bundle Mean condensation heat-transfer coefficient for a tube in a row of tubes Heat-transfer coefficient for condensation on a vertical tube Condensation coefficient from Boko-Kruzhilin correlation Condensation heat transfer coefficient for stratified flow in tubes Local condensing film coefficient, partial condenser Convective boiling-heat transfer coefficient... 

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) ... 

Figure 11-8. A schematic representation of the local surface conditions for heat transfer from a solid body with surface temperature T0 to a gas stream when there is a condensed liquid film on the body surface. As explained in the text, this leads to an approximate boundary condition on the surface S of mixed type (11 -98).

As indicated in Qhap. 13 all fluids are bounded at the retaining walls by a film of stagnant fluid. Heat must be transferred through these films by conduction. The films are very thin, their thicknesses cannot be easily measured, and hence the thickness L which is involved in the resistance of the film cannot be determined directly. In order to avoid this difficulty, the resistances of fluid films have been correlated by expressing the resistance as 1/h in which h is the film coefficient of heat transfer. From commonly accepted heat-transfer coefficients the apparent film thickness varies from about 0.1 for gases to about 0.0001 in. for condensing steam. If the conduction equation is applied to the transfer of heat from a fluid into a solid partition wall and into another fluid, the conduction equation takes the following form ... 

One of the requirements of this process is that the melt maintain good contact with the chill roU, ie, air must not pass between the film and the roU. Otherwise, air insulates the plastic and causes it to cool at a rate different from the rest of the plastic and this spoils the appearance of an otherwise satisfactory product. The melt should not emit volatiles, which condense on the chill roU, reduce heat transfer, and mar the film s appearance. The cast film process allows the use of a higher melt temperature than is characteristic of the blown film process. The higher temperature imparts better optical properties. 

Of these special surfaces, only the double-fluted tube has seen extended services. Most of the gain in heat-transfer coefficient is due to the condensing side the flutes tend to collect the condensate and leave the lauds bare [Caruavos, Proc. First Int. Symp. Water Desalination, 2, 205 (1965)]. The coudeusiug-film coefficient (based on the actual outside area, which is 28 percent greater than the nominal area) may be approximated from the equation... 

When a saturated vapour is brought into contact with a cool surface, heat is transferred from the vapour to the surface and a film of condensate is produced. 

These expressions give point values of h and Nux at x = x. It is seen that the coefficient decreases from a theoretical value of infinity at the top as the condensate film thickens. The mean value of the heat transfer coefficient over the whole surface, between r = 0 and jc = x is 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. 

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. 

If the degree of superheat is large, it will be necessary to divide the temperature profile into sections and determine the mean temperature difference and heat-transfer coefficient separately for each section. If the tube wall temperature is below the dew point of the vapour, liquid will condense directly from the vapour on to the tubes. In these circumstances it has been found that the heat-transfer coefficient in the superheating section is close to the value for condensation and can be taken as the same. So, where the amount of superheating is not too excessive, say less than 25 per cent of the latent heat load, and the outlet coolant temperature is well below the vapour dew point, the sensible heat load for desuperheating can be lumped with the latent heat load. The total heat-transfer area required can then be calculated using a mean temperature difference based on the saturation temperature (not the superheat temperature) and the estimated condensate film heat-transfer coefficient. 

This method takes advantage of the rough proportionality between heat and mass transfer coefficients according to the Chilton-Colburn analogy, and employs only heat transfer coefficients for the process of condensation from a mixture. The sensible heat of the vapor is transferred through the gas film... 

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