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.

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.

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.

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.

Effects of Vapor Superheat and Condensate Subcooling on Laminar Film Condensation

1999 ◽  
Vol 122 (1) ◽  
pp. 192-196 ◽  
Author(s):  
J. Mitrovic
Keyword(s):  
Heat Transfer ◽  
Single Phase ◽  
Saturated Vapor ◽  
Interfacial Shear ◽  
Film Condensation ◽  
Sensible Heat ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Condensation Model ◽  
The Heat Transfer Coefficient

Nusselt’s model is employed to illustrate the effects of vapor superheat and condensate subcooling on laminar film condensation occurring under simultaneous actions of gravity and interfacial shear. The vapor superheat affects the condensation kinetics in cooperation with heat transfer in both phases. Under comparable conditions, the condensate film is thinner and the heat transfer coefficient larger for superheated than for saturated vapor. The heat flux on the cooling surface arising from the sensible heat of condensate increases as the critical point of the condensing substance is approached and, at this point, the Nusselt condensation model gives the single-phase boundary layer solutions. [S0022-1481(00)00701-5]

Laminar Film Condensation on a Porous Vertical Wall With Uniform Suction Velocity

1964 ◽  
Vol 86 (4) ◽  
pp. 481-489 ◽  
Author(s):  
K. C. Jain ◽  
S. G. Bankoff
Keyword(s):  
Heat Capacity ◽  
Vertical Wall ◽  
Power Series Expansion ◽  
Porous Wall ◽  
Film Condensation ◽  
Suction Velocity ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Constant Suction ◽  
Prandtl Numbers

A perturbation method developed by Chen for laminar film condensation on a vertical, constant-temperature wall, taking into account condensate subcooling and vapor drag, is refined and extended to the case where some of the condensate is sucked off at constant velocity through a porous wall. The refinement consists of a single, rather than a double, power-series expansion in the heat capacity and the acceleration parameters. The extension consists of an exact solution of the Nusselt problem with constant suction velocity, followed by a perturbation procedure to take into account the heat capacity and acceleration effects. The results show that substantial increases in heat transfer can be effected in this manner, especially at high Prandtl numbers.

A Boundary-Layer Treatment of Laminar-Film Condensation

1959 ◽  
Vol 81 (1) ◽  
pp. 13-18 ◽  
Author(s):  
E. M. Sparrow ◽  
J. L. Gregg
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Prandtl Number ◽  
Vertical Plate ◽  
Film Condensation ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Prandtl Numbers ◽  
Mathematical Techniques

The problem of laminar-film condensation on a vertical plate is attacked using the mathematical techniques of boundary-layer theory. Starting with the boundary-layer (partial differential) equations, a similarity transformation is found which reduces them to ordinary differential equations. Energy-convection and fluid-acceleration terms are fully accounted for. Solutions are obtained for values of the parameter cpΔT/hfg between 0 and 2 for Prandtl numbers between 1 and 100. These solutions take their place in the boundary-layer family along with those of Blasius, Pohlhausen, Schmidt and Beckmann, and so on. Heat-transfer results are presented. It is found that the Prandtl-number effect, which arises from retention of the acceleration terms, is very small for Prandtl numbers greater than 1.0. Low Prandtl number (0.003–0.03) heat-transfer results are given in Appendix 2, and a greater effect of the acceleration terms is displayed.

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