Effects of Surface Tension on Film Condensation in a Porous Medium

1990 ◽  
Vol 112 (3) ◽  
pp. 751-757 ◽  
Author(s):  
A. Majumdar ◽  
C. L. Tien
Keyword(s):  
Boundary Layer ◽  
Surface Tension ◽  
Porous Medium ◽  
Film Condensation ◽  
Phase Zone ◽  
Two Phase ◽  
Liquid Zone ◽  
Darcy Velocity ◽  
Characteristic Boundary ◽  
Surface Tension Forces

In the process of film condensation in a porous medium, the thermodynamics of phase equilibria requires the existence of a two-phase zone lying between the liquid and the vapor regions. In the two-phase zone, solutions of the conservation equations indicate a boundary-layer profile for the capillary pressure. The liquid zone is analyzed using three models, which assume either slip or no slip at the wall and Darcy velocity or no shear at the interface with the two-phase zone. The results show that the condition of no slip at the wall must be satisfied in all cases except where the thickness of the liquid zone is much larger than the characteristic boundary layer in the porous medium. At the interface with the two-phase zone, the assumption of no shear is more realistic than that of an imposed Darcy velocity, in conjunction with no-slip condition at the wall. Comparisons with experiments suggest that the drag on the liquid film due to surface tension is significant for permeabilities lower than 10−7 m2. A dimensionless group, characterizing viscous flow due to surface tension forces, is introduced in this study.

Two-Phase Boundary Layer Treatment for Subcooled Free-Convection Film Boiling Around a Body of Arbitrary Shape in a Porous Medium

1987 ◽  
Vol 109 (4) ◽  
pp. 997-1002 ◽  
Author(s):  
A. Nakayama ◽  
H. Koyama ◽  
F. Kuwahara
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Free Convection ◽  
Phase Boundary ◽  
Flat Plate ◽  
Arbitrary Shape ◽  
Film Boiling ◽  
Two Phase ◽  
The One ◽  
Axisymmetric Bodies

The two-phase boundary layer theory was adopted to investigate subcooled free-convection film boiling over a body of arbitrary shape embedded in a porous medium. A general similarity variable which accounts for the geometric effect on the boundary layer length scale was introduced to treat the problem once for all possible two-dimensional and axisymmetric bodies. By virtue of this generalized transformation, the set of governing equations and boundary conditions for an arbitrary shape reduces into the one for a vertical flat plate already solved by Cheng and Verma. Thus, the numerical values furnished for a flat plate may readily be tranlsated for any particular body configuration of concern. Furthermore, an explicit Nusselt number expression in terms of the parameters associated with the degrees of subcooling and superheating has been established upon considering physical limiting conditions.

Laminar Filmwise Condensation on Horizontal Disk Embedded in Porous Medium With Suction at Wall

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
Tong-Bou Chang
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Liquid Film ◽  
Mechanical Energy ◽  
Disk Surface ◽  
Darcy Number ◽  
Nonlinear Ordinary Differential Equation ◽  
Phase Zone ◽  
Two Phase ◽  
Suction Parameter

This study performs a theoretical investigation into the problem of two-dimensional steady filmwise condensation flow on a horizontal disk embedded in a porous medium layer with suction at the disk surface. The analysis considers the case of a water-vapor system and is based on typical values of the relevant dimensional and dimensionless parameters. Due to the effects of capillary forces, a two-phase zone is formed between the liquid film and the vapor zone. The minimum mechanical energy concept is employed to establish the boundary condition at the edge of the horizontal disk and the Runge–Kutta shooting method is used to solve the second-order nonlinear ordinary differential equation of the liquid film. It is found that the capillary force and wall suction effects have a significant influence on the heat transfer performance. Specifically, the results show that the dimensionless heat transfer coefficient depend on the Darcy number Da, the Jacob number Ja, the effective Rayleigh number Rae, the effective Prandtl number Pre, the suction parameter Sw, and the capillary parameter Boc.

scholarly journals FEATURES OF THE FRACTIONAL-DIFFERENTIAL APPROACH IMPLEMENTATION TO DESCRIBE THE PROCESS OF FEEDING A TWO-PHASE ZONE DURING SOLIDIFICATION OF METALS AND ALLOYS

2021 ◽  
pp. 88-91
Author(s):  
Tatjana Selivyorstova ◽  
Vadim Selivyorstov ◽  
Yuliia Mala
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Nonlinear Equation ◽  
Mathematical Models ◽  
Single Phase ◽  
Phase Zone ◽  
Two Phase ◽  
Diffusion Type ◽  
Differential Approach ◽  
Fractional Differential

To describe filtration processes in complex dendritic-porous media, a number of fractional-differential mathematical models of diffusion type have been proposed.A nonlinear equation containing fractional Riemann-Liouville derivatives with respect to time is described, which can be used to correctly describe the single-phase filtration of a non-Newtonian fluid in a porous medium.

Pore-Scale Investigation of Two-Phase Drainage Process in a Microchannel

2013 ◽  
Author(s):  
Y. F. Yap ◽  
A. Goharzadeh ◽  
F. M. Vargas ◽  
J. C. Chai
Keyword(s):  
Surface Tension ◽  
Porous Medium ◽  
Level Set Method ◽  
Level Set ◽  
Pore Scale ◽  
Middle Section ◽  
Scale Level ◽  
Two Phase ◽  
Flow And Transport

This article presents a level-set method to investigate two-phase drainage of oil by water in microchannel with numerous blockages in the middle section, mimicking a porous medium of different permeability at the pore-scale level. The presented framework is intended for gaining an understanding of the nature of flow and transport at the pore-scale level. In particular, the sweeping efficiency for the drainage process is parametrically studied for system with different viscosities and surface tension.

The Influence of Thermocapillary Flow on Heat Transfer in Film Condensation

1973 ◽  
Vol 95 (1) ◽  
pp. 21-24 ◽  
Author(s):  
J. D. Cary ◽  
B. B. Mikic
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Flat Surface ◽  
Practical Interest ◽  
Thermocapillary Flow ◽  
Film Condensation ◽  
Finite Difference Technique ◽  
Relative Measure ◽  
Circular Arcs ◽  
Surface Tension Forces

The influence of fluid flow—induced by surface-tension forces—on heat transfer through a condensate film broken by non-wetting strips was considered. The film was modeled as a two-dimensional layer on an isothermal, vertical flat surface; the layer has a flat midsection with circular arcs at the edges. The solution was obtained by a finite-difference technique for several values of the Marangoni number (Nm) which provides a relative measure of the surface-tension forces and of the Biot number (Bi) which provides a relative measure of the heat transfer at the liquid–vapor interface. The range of parameters covered by this work transcends the limits of most practical interest for water. The results show that internal thermocapillary circulation causes modest increases in heat transfer. It is concluded that thermocapillary flow might be an important factor in determining the geometry of channeled condensate films.

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.

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