Laminar Film Condensation on a Nanosphere

2012 ◽  
Vol 3 (1) ◽  
Author(s):  
J. A. Esfahani ◽  
S. Koohi-Fayegh
Keyword(s):  
Film Thickness ◽  
Liquid Film ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Liquid Film Thickness ◽  
Film Condensation ◽  
Runge Kutta Method ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Liquid Mass Flow Rate

The present work investigates an analytical study on the problem of laminar film condensation on a nanosphere. Due to the microscale interaction, the problem is analyzed by taking into account the effects of slip in velocity and jump in temperature. A relation is derived for the liquid film thickness in the form of a nonlinear differential equation which is solved numerically using the fourth order Runge–Kutta method. Finally, the effect of velocity slip and temperature jump on different condensation parameters including the liquid film thickness, velocity and temperature profiles, Nusselt number, and liquid mass flow rate is discussed. It is found that the increase in the velocity slip and temperature jump results in a thinner liquid film and therefore increases the heat transfer coefficient.

Laminar Film Condensation From a Steam-Air Mixture Undergoing Forced Flow Down a Vertical Surface

1971 ◽  
Vol 93 (3) ◽  
pp. 297-304 ◽  
Author(s):  
V. E. Denny ◽  
A. F. Mills ◽  
V. J. Jusionis
Keyword(s):  
Liquid Film ◽  
Numerical Solution ◽  
Finite Difference Methods ◽  
Vertical Surface ◽  
Forced Flow ◽  
Film Condensation ◽  
Two Phase ◽  
Noncondensable Gas ◽  
Laminar Film ◽  
Laminar Film Condensation

An analytical study of the effects of noncondensable gas on laminar film condensation of vapor under going forced flow along a vertical surface is presented. Due to the markedly nonsimilar character of the coupled two-phase-flow problem, the set of parabolic equations governing conservation of momentum, species, and energy in the vapor phase was solved by means of finite-difference methods using a forward marching technique. Interfacial boundary conditions for the numerical solution were extracted from a locally valid Nusselt-type analysis of the liquid-film behavior. Locally variable properties in the liquid were treated by means of the reference-temperature concept, while those in the vapor were treated exactly. Closure of the numerical solution at each step was effected by satisfying overall mass and energy balances on the liquid film. A general computer program for solving the problem has been developed and is applied here to condensation from water-vapor–air mixtures. Heat-transfer results, in the form q/qNu versus x, are reported for vapor velocities in the range 0.1 to 10.0 fps with the mass fraction of air ranging from 0.001 to 0.1. The temperature in the free stream is in the range 100–212 deg F, with overall temperature differences ranging from 5 to 40 deg F. The influence of noncondensable gas is most marked for low vapor velocities and large gas concentrations. The nonsimilar character of the problem is especially evident near x = 0, where the connective behavior of the vapor boundary layer is highly position-dependent.

Paper 6: Effect of Vapour Drag on Laminar Film Condensation on a Vertical Surface

1965 ◽  
Vol 180 (10) ◽  
pp. 280-287 ◽  
Author(s):  
Y. R. Mayhew ◽  
D. J. Griffiths ◽  
J. W. Phillips
Keyword(s):  
Reynolds Number ◽  
Liquid Film ◽  
Atmospheric Pressure ◽  
Vertical Surface ◽  
Simple Theory ◽  
Experimental Results ◽  
Film Condensation ◽  
Laminar Film ◽  
Laminar Film Condensation

A simple theory is presented for laminar film condensation of a pure vapour on a vertical surface which takes account of the drag induced on the liquid film by the flow of the condensing vapour. Experiments were carried out with steam at atmospheric pressure condensing inside a vertical 1.824 in diameter tube 8 in high. The downward vapour velocity was varied from 5 to 150 ft/s, the corresponding range of the film Reynolds number at the bottom of the tube being 200-500. Experimental results agreed well with the theory.

Effect of Vapour Drag on Laminar Film Condensation on a Vertical Rectangular Fin

1993 ◽  
Vol 207 (1) ◽  
pp. 63-69
Author(s):  
H Kazeminejad
Keyword(s):  
Heat Transfer ◽  
Film Thickness ◽  
Transfer Rate ◽  
Relative Effect ◽  
Film Condensation ◽  
Friction Drag ◽  
Condensate Film ◽  
Fin Efficiency ◽  
Laminar Film ◽  
Laminar Film Condensation

A simple theory is presented for laminar film condensation of a pure vapour on a vertical rectangular fin which takes account of drag induced on the liquid film by the flow of the condensing vapour. Under these conditions, the governing conjugate differential equations for the fin and condensate flow are solved numerically to determine the fin temperature and condensate film thickness distributions. For the range of parameters investigated, it was found that the reduction in condensate thermal resistance due to vapour shear significantly enhances the heat-transfer rate to the fin and decreases the fin efficiency. The model also provides a clear picture of the relative effect of the gravity force, friction drag and momentum drag on the performance of the fin.

Laminar Film Condensation on a Vertical Melting Surface

1976 ◽  
Vol 98 (1) ◽  
pp. 108-113 ◽  
Author(s):  
M. Epstein ◽  
D. H. Cho
Keyword(s):  
Liquid Film ◽  
Saturated Vapor ◽  
Previous Treatment ◽  
Film Condensation ◽  
Full Account ◽  
Component System ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Melting Surface ◽  
Prandtl Numbers

Laminar film condensation of a saturated vapor on a vertical melting surface is treated theoretically, with emphasis on departures from a previous treatment produced by: (a) arbitrary liquid Prandtl numbers and (b) condensation-melting systems involving two materials of immiscible liquids. An integral method is utilized which takes full account of the effects of both liquid film inertia and shear force at the condensing vapor-liquid film interface. For a one-component system accurate numerical results for the melting rates are displayed graphically and define the range of validity of a simple treatment of this problem based on Nusselt’s method. For a two-component system, illustrative calculations are made for the condensation of a refrigerant vapor on melting ice.

Effect of Tube Geometry and Curvature on Film Condensation in the Presence of a Noncondensable Gas

2014 ◽  
Vol 7 (1) ◽  
Author(s):  
Huijun Li ◽  
Wenping Peng ◽  
Yingguang Liu ◽  
Chao Ma
Keyword(s):  
Heat Transfer ◽  
Film Thickness ◽  
Liquid Film ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Liquid Film Thickness ◽  
Film Condensation ◽  
Tube Surface ◽  
Noncondensable Gas ◽  
Tube Geometry

Based on the double boundary layer theory, a generalized mathematical model was developed to study the distributions of gas film, liquid film, and heat transfer coefficient along the tube surface with different geometries and curvatures for film condensation in the presence of a noncondensable gas. The results show that: (i) for tubes with the same geometry, gas film thickness, and liquid film thickness near the top of the tube decrease with the increasing of curvature and the heat transfer rate increases with it. (ii) For tubes with different geometries, one need to take into account all factors to compare their overall heat transfer rate including gas film thickness, liquid film thickness and the separating area. Besides, the mechanism of the drainage and separation of gas film and liquid film was analyzed in detail. One can make a conclusion that for free convection, gas film never separate since parameter A is always positive, whereas liquid film can separate if parameter B becomes negative. The separating angle of liquid film decreases with the increasing of curvature.

Flow Regimes for Laminar Film Condensation on a Vertical Plate With an Upward Vapor Flow

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Kentaro Kanatani
Keyword(s):  
Nusselt Number ◽  
Film Thickness ◽  
Average Nusselt Number ◽  
Vertical Plate ◽  
Film Condensation ◽  
Integral Model ◽  
Vapor Flow ◽  
Plate Length ◽  
Laminar Film ◽  
Laminar Film Condensation

Abstract Laminar film condensation on a vertical plate with an upward vapor flow is studied. An approximate integral model of the condensate film and the boundary layer of the vapor is numerically solved, taking into account both gravity and interfacial shear. Here, three types of solution are examined: (i) zero film thickness at the bottom; (ii) zero flowrate with a finite film thickness at the bottom; and (iii) negative flowrates at the bottom. The film thickness and the average Nusselt number are shown as functions of the distance along the plate and the plate length, respectively. The terminal lengths of the solutions of the types (i) and (ii) are calculated against the degree of the subcooling. Moreover, the results are compared with those derived using the approximation method where the shearing stress on the vapor–liquid interface is composed of only the momentum transferred by the suction mass (the Shekriladze–Gomelauri approach). It is found that the average Nusselt number is well described by the Shekriladze–Gomelauri model in the range of the solution type (ii), while the average Nusselt number for the thinnest-film solution of the type (iii) is asymptotically consistent with the Shekriladze–Gomelauri value for long plates.

scholarly journals Two-Phase Region Effect on Film Condensation on an Inclined Plate Embedded in a Porous Medium

2020 ◽  
Vol 78 (2) ◽  
pp. 67-84
Author(s):  
Yee Lee Yeu ◽  
Alexander Gorin
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Film Thickness ◽  
Liquid Film ◽  
Phase Region ◽  
Liquid Film Thickness ◽  
Film Condensation ◽  
Two Phase ◽  
Region Effect

Film condensation in a porous medium has been receiving increasing attention due to its wide range of heat transfer applications. Some examples of these practical applications are distillation, drying technology, geothermal energy, cooling towers, heat exchangers, and air conditioning. One of the characteristic features of film condensation in porous media is the formation of a two-phase zone separating the liquid film and the vapour zone due to capillary pressure. In this paper, a physico-mathematical model of liquid film condensation on a surface embedded in a porous medium with a two-phase region effect is developed and presented. The model is based on momentum and continuity equations as applied to the liquid film and the two-phase flow region supplemented with the Darcy flow assumption and assumptions on the Leverette J-function and the saturation behaviour near the edge of the liquid film. The developed model allows a simple analytical solution to the problem in distinction to semi-analytical and numerical solutions published by different authors. From the model developed, it shows that the presence of the two-phase region decreases the liquid film thickness. By taking the capillary effects into consideration results in higher heat transfer and condensation rates due to the decrease in the liquid film thickness. The presented model yields good agreement when compared to the theoretical results and experimental data by other authors. The developed model addresses the fundamental concepts of phase transition in porous media which can effectively find applications in many areas.

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