The two phase boundary layer in laminar film condensation

1961 ◽  
Vol 2 (1-2) ◽  
pp. 69-82 ◽  
Author(s):  
J.C.Y. Koh ◽  
E.M. Sparrow ◽  
J.P. Hartnett
Keyword(s):  
Boundary Layer ◽  
Phase Boundary ◽  
Film Condensation ◽  
Two Phase ◽  
Laminar Film ◽  
Laminar Film Condensation

An Integral Treatment of Two-Phase Boundary Layer in Film Condensation

1961 ◽  
Vol 83 (3) ◽  
pp. 359-362 ◽  
Author(s):  
J. C. Y. Koh
Keyword(s):  
Boundary Layer ◽  
Phase Boundary ◽  
Film Condensation ◽  
Two Phase ◽  
Boundary Layer Problem ◽  
Boundary Layer Equations ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Integral Treatment ◽  
Two Parameters

By using the integral method, the task of solving the complicated two-phase boundary-layer differential equations in laminar-film condensation has been reduced to the simple work of solving an algebraic equation. It was shown analytically that the parameter [(ρμ)L/(ρμ)v]1/2 can be removed from the film-condensation problem and hence only two parameters, cpΔT/hfg and Pr, are involved. The calculated results in heat transfer and condensate flow rates agree very well with the results from the exact solution of the boundary-layer equations. With [(ρμ)v/(ρμ)L]1/2 remaining as a parameter, it is believed that the present method can be used to solve the analogous two-phase boundary-layer problem in laminar film boiling.

Revisit of Laminar Film Condensation Boundary Layer Theory for Solution of Mixed Convection Condensation With or Without Noncondensables

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Y. Liao
Keyword(s):  
Boundary Layer ◽  
Mixed Convection ◽  
Forced Convection ◽  
Vapor Condensation ◽  
Boundary Layer Theory ◽  
Film Condensation ◽  
Two Phase ◽  
Boundary Layer Equations ◽  
Laminar Film ◽  
Laminar Film Condensation

This work presents a unique and unified formulation to solve the laminar film condensation two-phase boundary layer equations for the free, mixed, and forced convection regimes in the absence or presence of noncondensables. This solution explores the vast space of mixed convection across the four cornerstones of laminar film condensation boundary layer theory, two established by Koh for pure vapor condensation in the free or forced convection regimes and the other two established by Sparrow corresponding to condensation with noncondensables. This formulation solves the space of mixed convection completely with Koh and Sparrow’s solutions shown to be merely four specific cases of the current solution.

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.

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