A Two-Phase Boundary Layer and Its Drag-Reduction Characteristics

1962 ◽  
Vol 29 (2) ◽  
pp. 408-414 ◽  
Author(s):  
E. M. Sparrow ◽  
V. K. Jonsson ◽  
E. R. G. Eckert
Keyword(s):  
Boundary Layer ◽  
Phase Boundary ◽  
Liquid Flow ◽  
Single Phase ◽  
Free Stream ◽  
Stream Velocity ◽  
Two Phase ◽  
Drag Forces ◽  
Liquid Boundary ◽  
Reduction Characteristics

Consideration is given to coexisting gas and liquid boundary layers which occur when a gas is injected at the surface of a flat plate into a free-stream liquid flow. It is postulated that the gas forms a continuous film over the plate surface. The problem can be formulated exactly within the framework of laminar boundary-layer theory. Solutions have been carried out for a range of values of blowing velocity and of a fluid property parameter (ρμ) L / (ρμ)g. It is demonstrated that the drag forces associated with the two-phase boundary layer are much smaller than those for the single-phase liquid flow. For example, for a blowing velocity which is 0.001 of the free-stream velocity and a gas Reynolds number of 105, the over-all drag calculation yields a value which is 0.0205 of the single-phase drag force. The effect of evaporation at the gas-liquid interface is analyzed and found to be small at temperatures which are not too close to saturation.

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.

scholarly journals Supercapillary Architecture‐Activated Two‐Phase Boundary Layer Structures for Highly Stable and Efficient Flow Boiling Heat Transfer

2019 ◽  
Vol 32 (2) ◽  
pp. 1905117 ◽  
Author(s):  
Wenming Li ◽  
Zuankai Wang ◽  
Fanghao Yang ◽  
Tamanna Alam ◽  
Mengnan Jiang ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Phase Boundary ◽  
Boiling Heat Transfer ◽  
Flow Boiling ◽  
Two Phase ◽  
Layer Structures ◽  
Flow Boiling Heat Transfer

Eddy Viscosity Distributions in Compressible Turbulent Boundary Layers with Injection

1971 ◽  
Vol 22 (2) ◽  
pp. 169-182 ◽  
Author(s):  
L. C. Squire
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Mixing Length ◽  
Carbon Dioxide Injection ◽  
Displacement Thickness ◽  
Porous Surfaces ◽  
Injection Ratio

SummaryShear stress, eddy viscosity and mixing length distributions have been obtained from measured boundary-layer developments over porous surfaces with air and carbon dioxide injection at Mach numbers up to M=3·6. It is found that, if the eddy viscosity is non-dimensionalised by dividing by the product of the free-stream velocity and the kinematic displacement thickness then this non-dimensional ratio is almost independent of injection ratio, but decreases slightly with Mach number.

scholarly journals Prediction of Heat Transfer From Laminar Boundary Layers, With Emphasis on Large Free-Stream Velocity Gradients and Highly Cooled Walls

1966 ◽  
Vol 88 (3) ◽  
pp. 249-256 ◽  
Author(s):  
L. H. Back ◽  
A. B. Witte
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Gradient ◽  
Free Stream ◽  
Variable Density ◽  
Similarity Solutions ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Gradient Parameter

Laminar boundary-layer heat transfer and shear-stress predictions from existing similarity solutions are extended in an approximate way to perfect gas flows with a large free-stream velocity gradient parameter β and variable density-viscosity product ρμ across the boundary layer resulting from a highly cooled wall. The dimensionless enthalpy gradient at the wall gw′, to which the heat flux is related, is found not to vary appreciably with β. Thus the application of similarity solutions on a local basis to predict heat transfer from accelerated flows to an arbitrary surface may be a reasonable approximation involving a minimum amount of calculation time. Unlike gw′, the dimensionless velocity gradient at the wall fw″, to which the shear stress is related, is strongly dependent on β.

Two-phase boundary layer formation in a semi-infinite porous slab

1989 ◽  
Vol 4 (4) ◽  
pp. 395-420 ◽  
Author(s):  
John G. Burnell ◽  
Alex McNabb ◽  
Graham J. Weir ◽  
Roger Young
Keyword(s):  
Boundary Layer ◽  
Phase Boundary ◽  
Layer Formation ◽  
Two Phase ◽  
Boundary Layer Formation

Effects of Partial Slip on Chemically Reactive Solute Distribution in MHD Boundary Layer Stagnation Point Flow Past a Stretching Permeable Sheet

2015 ◽  
Vol 13 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Swati Mukhopadhyay
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Stream Velocity ◽  
Slip Parameter ◽  
Mhd Boundary Layer

Abstract This paper presents the magnetohydrodynamic (MHD) boundary layer stagnation point flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet in presence of partial slip. With the help of similarity transformations, the partial differential equations corresponding to momentum and the concentration equations are transformed into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity and the stretching velocity. Velocity decreases with the increasing magnetic parameter when the free-stream velocity is less than the stretching velocity but the opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. With increasing velocity slip parameter, velocity increases when the free-stream velocity is greater than the stretching velocity. But the concentration decreases in this case. Concentration decreases with increasing mass slip parameter.

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