Laminar Film Condensation on a Sphere

1973 ◽  
Vol 95 (2) ◽  
pp. 174-178 ◽  
Author(s):  
J. W. Yang
Keyword(s):  
Horizontal Cylinder ◽  
Film Condensation ◽  
Stagnation Region ◽  
Similarity Transformations ◽  
Laminar Film ◽  
First Case ◽  
Laminar Film Condensation ◽  
Layer Analysis ◽  
Prandtl Numbers ◽  
Inertia Forces

A boundary-layer analysis is made for laminar film condensation on a sphere. Similarity transformations are made for two cases. The first case includes both the inertia forces and heat convection; the solutions are valid in the upper stagnation region. The second case excludes the inertia forces; the solutions are valid over the entire surface for high Prandtl numbers. Results of heat-transfer rate, condensation rate, and film thickness are presented. Comparisons with a vertical plate and a horizontal cylinder are discussed.

Laminar Condensation Heat Transfer on a Horizontal Cylinder

1959 ◽  
Vol 81 (4) ◽  
pp. 291-295 ◽  
Author(s):  
E. M. Sparrow ◽  
J. L. Gregg
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Horizontal Cylinder ◽  
Film Condensation ◽  
Number Range ◽  
Laminar Film Condensation ◽  
Layer Analysis ◽  
Inertia Forces

A boundary-layer analysis is made for laminar film condensation on a horizontal cylinder. The formulation includes both the inertia forces and energy convection terms, which are neglected in Nusselt’s simple theory. A similarity transformation, valid over most of the cylinder, is found which reduces the partial differential equations of the problem (the conservation laws) to ordinary differential equations. Numerical solutions of the resulting ordinary differential equations are available for the Prandtl number range from 0.003 to 100. Heat-transfer results are presented and discussed.

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.

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.

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.

Laminar film condensation on a thin finite thickness plate

10.2514/3.866 ◽  
1997 ◽  
Vol 11 ◽  
pp. 119-121
Author(s):  
Lorenzo Mottura ◽  
Luigi Vigevano ◽  
Marco Zaccanti ◽  
F. Mendez ◽  
G. Becerra ◽  
...  
Keyword(s):  
Finite Thickness ◽  
Film Condensation ◽  
Laminar Film ◽  
Laminar Film Condensation

Superheated laminar film condensation on a nonisothermal horizontal tube

10.2514/3.931 ◽  
1997 ◽  
Vol 11 ◽  
pp. 526-532
Author(s):  
V. R. Murthy ◽  
Yu-An Lin ◽  
Steven W. O' ◽  
Hara Har ◽  
Sheng-An Yang
Keyword(s):  
Horizontal Tube ◽  
Film Condensation ◽  
Laminar Film ◽  
Laminar Film Condensation
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