Laminar Film Condensation of a Flowing Vapor on a Horizontal Cylinder at Normal Gravity

1969 ◽  
Vol 91 (4) ◽  
pp. 495-501 ◽  
Author(s):  
V. E. Denny ◽  
A. F. Mills
Keyword(s):  
Boundary Layer ◽  
Normal Gravity ◽  
Numerical Solutions ◽  
Horizontal Cylinder ◽  
Vertical Surface ◽  
Film Condensation ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Fluid Properties ◽  
Finite Difference Analog

An analytical solution, based on the Nusselt assumptions, has been obtained for laminar film condensation of a flowing vapor on a horizontal cylinder. In so doing, a reference temperature for evaluating locally variable fluid properties is defined in the form Tr = Tw + α (Ts − Tw) and accounts for both the effects of fluid property variations and minor errors introduced by the assumptions in the analysis. Verification was obtained by comparison with exact numerical solutions based on a finite-difference analog to the conservation equations in boundary-layer form. In the analytical as well as the numerical developments, vapor drag was accounted for through an asymptotic solution of the vapor boundary layer under strong suction. It was found that, for angles up to 140 deg, there was less than a 2 percent discrepancy between the analytical predictions and the numerical results. As 180 deg is approached an increased discrepancy is expected due to a gross violation of the Nusselt assumptions. The values of the reference parameter α, which were previously derived for condensation on a vertical surface, were found to be appropriate for the horizontal cylinder as well.

Similar Solutions for Laminar Film Condensation with Adverse Pressure Gradients

1973 ◽  
Vol 95 (2) ◽  
pp. 268-270 ◽  
Author(s):  
P. M. Beckett
Keyword(s):  
Numerical Solutions ◽  
Saturated Vapor ◽  
Film Condensation ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Laminar Film ◽  
Approximate Models ◽  
Laminar Film Condensation ◽  
Similar Solutions

Steady two-dimensional laminar film condensation is investigated when the saturated vapor has the Falkner–Skan mainstream. Numerical solutions and approximate models are discussed with reference to other published work.

An Analytical Study of Laminar Film Condensation: Part 2—Single and Multiple Horizontal Tubes

1961 ◽  
Vol 83 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Michael Ming Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Horizontal Tube ◽  
Vertical Tube ◽  
Film Condensation ◽  
Transfer Coefficients ◽  
Inertia Effects ◽  
Horizontal Tubes ◽  
Laminar Film ◽  
Laminar Film Condensation

The boundary-layer equations for laminar film condensation are solved for (a) a single horizontal tube, and (b) a vertical bank of horizontal tubes. For the single-tube case, the inertia effects are included and the vapor is assumed to be stationary outside the vapor boundary layer. Velocity and temperature profiles are obtained for the case μvρv/μρ ≪ 1 and similarity is found to exist exactly near the top stagnation point, and approximately for the most part of the tube. Heat-transfer results computed with these similar profiles are presented and discussed. For the multiple-tube case, the analysis includes the effect of condensation between tubes, which is shown to be partly responsible for the high observed heat-transfer rate for vertical tube banks. The inertia effects are neglected due to the insufficiency of boundary-layer theory in this case. Heat-transfer coefficients are presented and compared with experiments. The theoretical results for both cases are also presented in approximate formulas for ease of application.

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.

scholarly journals Mixed-convection laminar film condensation on a semi-infinite vertical plate

1995 ◽  
Vol 300 ◽  
pp. 207-229 ◽  
Author(s):  
Jian-Jun Shu ◽  
Graham Wilks
Keyword(s):  
Vertical Plate ◽  
Body Force ◽  
Numerical Solutions ◽  
Force Convection ◽  
Film Condensation ◽  
Approximate Methods ◽  
Saturated Vapour ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Infinite Vertical Plate

The flow of a uniform stream of pure saturated vapour past a cold, semi-infinite vertical plate is examined. The formulation incorporates the limits of both pure forcedconvection and pure body-force-convection laminar film condensation. Detailed asymptotic and exact numerical solutions are obtained and comparisons drawn with approximate methods and experimental results reported in the literature.

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.

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