Condensation Heat-Transfer Phenomena

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 

Because of the higher heat-transfer rates, dropwise condensation would be preferred to Him condensation, but it is extremely difficult to maintain since most surfaces become wetted after exposure to a condensing vapor over an extended period of time. Various surface coatings and vapor additives have been used in attempts to maintain dropwise condensation, but these methods have not met with general success to date. Some of the pioneer work on drop condensation was conducted by Schmidt [26] and a good summary of the overall problem is presented in Ref. 27. Measurements of Ref. 35 indicate that the drop conduction is the main resistance to heat flow for atmospheric pressure and above. Nucleation site density on smooth surfaces can be of the order of 10 sites per square centimeter, and heat-transfer coefficients in the range of 170 to 290 kW/m2 °C [30,000 to 50,000 Btu/h ft2 °F] have been reported by a number of investigators. 

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 

Integrating and using the boundary condition that h = 0 at y = 0 gives 

The mass flow of condensate through any x position of the him is thus given by 

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Heat Transfer Correlations for External Condensation. Although the complexity of condensation heat transfer phenomena prevents a rigorous theoretical analysis, an external condensation for some simple situations and geometric configurations has been the subject of a mathematical modeling. The famous pioneering Nusselt theory of film condensation had led to a simple correlation for the determination of a heat transfer coefficient under conditions of gravity-controlled, laminar, wave-free condensation of a pure vapor on a vertical surface (either flat or tube). Modified versions of Nusselt s theory and further empirical studies have produced a list of many correlations, some of which are compiled in Table 17.23. 

It was shown that in heat transfer with phase change it is necessary to understand the phase-change phenomenon on the molecular level to model effectively the mass- and heat-transfer processes. An analytical expression for the rates of vaporization and condensation was developed. It was also shown that the assumption of a saturated vapor phase greatly simplified the calculation without a significant loss in accuracy for given examples. However, experimental verification of this simplified assumption is currently lacking. 

The molecnlar weight of water vapor (MW= 18) is less than that of air (MW= 29). As snch, the diffnsion of water vapor into the surrounding atmosphere, which consists of a mixtnre of water and air, leads to a buoyant force with upward macroscopic movement. The natural evaporation phenomenon is not only the effect of heat transfer but also a buoyancy-induced motion. The system is at steady state when the vapor pressure of the water at the surface is less than that in the air above, and the resulting condensation is governed by the slow process of molecular diffusion and lamilar flow. 

For an upward flow direction, the shear forces may influence the downward-flow of the condensate, causing an increase of the condensate film thickness. Therefore, the heat transfer coefficient under such conditions shall decrease up to 30 percent compared to the result obtained using the same correlation as the upward-flowing vapor. If the vapor velocity increases substantially, the so-called flooding phenomenon may occur. Under such condition, the shear forces completely prevent the downward condensate flow and flood (block) the tube with the condensate. Prediction of the flooding conditions is discussed by Wallis, as reported by Butterworth [81]. 

Additional complications arise if there is heat transfer from one phase to another such as that encoimtered in the tubes of a condenser or boiler. Under these conditions, the mass flowrate of each phase is progressively changing as a result of the vapoin condensing or the liquid vaporising. However, this phenomenon is of little relevance to the flow of gas and non-Newtonian liquid mixtures. 

Phosphorus is known as an effective char promoter. Charring limits the release of fuels to the flame and therefore reduces the heat released. Moreover, the char accumulates on the surface of the material and can act as a protective layer which limits the heat transfer from the flame to the condensed phase and the gas transfer from the pyrolysis zone to the flame. This phenomenon is called the barrier effect. Nevertheless, it should be noted that the presence of char is not a sufficient condition to observe an effective barrier effect. Its structure (cohesion, porosity, thickness) is also veiy important but rarely studied. Thermal stability is another important parameter to assess the reaction to fire of a material. Indeed, the higher is the degradation temperature of a polymer, the greater is the heat required to start its pyrolysis. Table 12.2 lists the effects of phosphorus-containing groups on the thermal stability and charring for a variety of polymers. 

The opposite problem to steam condensate backup is blowout of uncondensed steam through the reboiler and out the condensate drain line. This phenomenon causes a loss in heat transfer entirely out of proportion to what might be expected. Literally half of a reboiler s duty can be lost by an apparently small amount of steam blowing out the condensate drain line. 

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