Cylinder film condensation

Film condensation on a horizontal tube. For a curvilinear surface, in particular, for a horizontal circular cylinder along which a condensate film flows, the angle 6 is a nonconstant variable. By taking into account the fact that 6(6) d, where d is the diameter of a circular cylinder, and proceeding by analogy with (5.7.7), one can readily obtain the following formula for the heat transfer coefficient averaged over the external surface of the tube provided that the flow in the condensate film is laminar [200] ... 

K. E. Hassan and M. Jakob, Laminar Film Condensation of Pure Saturated Vapors on Inclined Circular Cylinders, 7 Heat Transfer, 80, pp. 887-894,1958. 

Vertical Flat Plates. Following the earlier work by Bromley [190] on cylinders (see below), Hsu and Westwater [191] derived an expression for laminar film boiling on a vertical plate that is analogous to that for laminar film condensation. The average value of hc over a plate of height L is given by... 

Steam Supply and Condensate Removal All cylinder dryers are heated by the steam condensing inside the sheet because of its efficiency (heat-transfer coefficient for film condensation of steam ranges from 5,700 to 17,000 W/m K (1,000-3,(XX) Btu/h ft °F). In the early days of papermaking, steam pressures as low as 14-21 kPa (2-3 psi) were used after World War n, the new machines for Kraft papers were made... 

Film-condensation coefficients outside horizontal cylinders. The analysis of Nusselt can also be extended to the practical case of condensation outside a horizontal tube. For a single tube the film starts out with zero thickness at the top of the tube and increases in thickness as it flows around to the bottom and then drips off. If there is a... 

The second type of thin-film evaporator, termed a wiped-film evaporator, introduces feed material on a heated waU of a cylinder. Rotating wiper blades continuously spread the feed along the inner waU of the cylinder to maintain uniformity of thickness and to ensure contact with the heated surface. The volatile components are driven off and coUected on an internal chilled condenser surface. The condensate or distUlate is removed continuously. At the end of the process, the residual becomes dry and heavy and drops to the bottom of the unit for removal. The wiped-film evaporator is best suited for treatment of viscous or high-solids content feed. 

Over the years, vapour adsorption and condensation in porous materials continue to attract a great deal of attention because of (i) the fundamental physics of low-dimension systems due to confinement and (ii) the practical applications in the field of porous solids characterisation. Particularly, the specific surface area, as in the well-known BET model [I], is obtained from an adsorbed amount of fluid that is assumed to cover uniformly the pore wall of the porous material. From a more fundamental viewpoint, the interest in studying the thickness of the adsorbed film as a function of the pressure (i.e. t = f (P/Po) the so-called t-plot) is linked to the effort in describing the capillary condensation phenomenon i.e. the gas-Fadsorbed film to liquid transition of the confined fluid. Indeed, microscopic and mesoscopic approaches underline the importance of the stability of such a film on the thermodynamical equilibrium of the confined fluid [2-3], In simple pore geometry (slit or cylinder), numerous simulation works and theoretical studies (mainly Density Functional Theory) have shown that the (equilibrium) pressure for the gas/liquid phase transition in pores greater than 8 nm is correctly predicted by the Kelvin equation provided the pore radius Ro is replaced by the core radius of the gas phase i.e. (Ro -1) [4]. Thirty year ago, Saam and Cole [5] proposed that the capillary condensation transition is driven by the instability of the adsorbed film at the surface of an infinite... 

This result is in a qualitative agreement with the experimental t-plot of Ar adsorption at 87 K on MCM 41 samples (see Figure 2(b)) using the data given in reference [13], As for simulation data, we assume that the density of the adsorbate equals that of the 3D-liquid and we have determined the thickness of the adsorbed film as the ratio of the adsorbed volume with the surface of the sample. Assuming pores of MCM 41 are cylinders, the specific surface S of each sample was determined via the relation between the porous volume V (given by the adsorbed amount after capillary condensation) and the diameter d of the pores S = 4V/d. Comparison of the different t-curves indicates that there is a pore size (5.1 nm) above which no confinement effect occurs on multilayer adsorption. Below this value, the thickness of the adsorbed film increases as the pore diameter decreases, t-curves are often analysed with the Frenkel-Halsey-Hill equation [14] /n... 

Using an analysis similar to Nusselt s theory on filmwisc condensation presented in the next section, Bromley developed a theory for the prediction of heat flux for stable film boiling on the outside of a horizontal cylinder. The heat Ilux for film boiling on a horizontal cylinder or sphere of diameter D is given by... 

The inner reference cylinder can be moved vertically and maintained concentric with the outer section. With the inner cylinder raised, a metal him can be evaporated to form the outer cylinder of the capacitor. The reference surface is prepared by coating the outside of the glass cylinder with a mixture of stannous oxide+1% antimony pentoxide. For most evaporated films, the condenser has a capacity of 30 pf. It is essential to screen effectively from electromagnetic and electrostatic interference. This is done by earthing the filament, an inner stannous oxide coating and an outer coating of liquid platinum. 

The distilland (sample) is added to the top and allowed to flow by the force of gravity down the surface in a thin film. The still usually consists of two vertical concentric cylinders, one being the evaporator and the other the condenser. Most of the sample is stored at low temperature and only the portion that is in immediate contact with the evaporator is heated and then only for a few seconds (10-50). Most falling films are from 0.1 to 2.0 mm thick. The efficiency is better than that of all but the smallest batch apparatus with f values approaching 1 and having one theoretical plate between the evaporator and the condenser. A value of 5-6 g/secW is reasonable with small units. From 5-10 % of the sample is distilled in one pass. Such a still is shown in Figure 7-3. 

An extension of this model to take account of turbulence is described by Klimenko [194], Horizontal Cylinders. The horizontal cylinder has been the most widely studied case of film boiling. Again, there is a strong analogy with condensation (see Fig. 15.76ft) and the classical expression for this case is that due to Bromley [190] as follows ... 

Complete details about the method of construction of 3-D porous networks through Monte Carlo simulation can be found elsewhere [10] similarly, the precise algorithm employed to replicate sorption processes in porous networks has been reported somewhere else [11]. Here, we will only mention several key aspects regarding these porous network and sorption simulations. First, the critical conditions required for cavities (hollow spheres) and necks (hollow cylinders open at both ends) to be fully occupied by either condensate or vapor have been calculated by means of the Broekhoff-de Boer (BdB) equation [12], while the thickness of the adsorbed film has been approximated via the Harkins-Jura equation [13]. Some other important assumptions that are made in this work are (i) the pore volume is exclusively due to sites (ii) bonds are considered as volumeless windows that communicate neighboring sites (ili) bonds can merge into a site without suffering of any geometrical interference with adjacent throats. 

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