Non-equilibrium flow through a nozzle

1963 ◽  
Vol 17 (1) ◽  
pp. 126-140 ◽  
Author(s):  
P. A. Blythe
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Vibrational Energy ◽  
Freezing Point ◽  
Nozzle Geometry ◽  
Equilibrium Flow ◽  
Boundary Layer Region ◽  
Suitable Boundary Condition ◽  
Flow Through ◽  
Layer Region

Vibrationally relaxing flow through a nozzle is examined in the case when the amount of energy in the lagging mode is small. It is shown that there exists a ‘boundary-layer’ region in which relatively large departures from equilibrium occur. The position of this region is given by the type of criterion that has previously been used to predict the onset of ‘freezing’. An analytical solution for the distribution of the vibrational energy in the nozzle is obtained for a particular nozzle geometry, and an expression for the final asymptotic ‘frozen’ value of the vibrational energy far downstream is found. This asymptotic solution can be obtained from conditions at the ‘freezing’ point provided a suitable boundary condition is applied there.

The Effect of Magnetic Field on Compressible Boundary Layer by Homotopy Analysis Method

2021 ◽  
Vol 88 (1-2) ◽  
pp. 125
Author(s):  
R. Madhusudhan ◽  
Achala L. Nargund ◽  
S. B. Sathyanarayana
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Adverse Pressure Gradient ◽  
Analysis Method ◽  
Boundary Layer Region ◽  
Homotopy Analysis ◽  
Curve Singularities ◽  
Large Injection ◽  
Layer Region

We analyse the effect of applied magnetic field on the flow of compressible fluid with an adverse pressure gradient. The governing partial differential equations are solved analytically by Homotopy analysis method (HAM) and numerically by finite difference method. A detailed analysis is carried out for different values of the magnetic parameter, where suction/ injection is imposed at the wall. It is also observed that flow separation is seen in boundary layer region for large injection. HAM is a series solution which consists of a convergence parameter h which is estimated numerically by plotting <em>h</em> curve. Singularities of the solution are identified by Pade approximation.

Role of mixed nanofluids on fluid flow and intensify energy transfer in a boundary layer region driven by a free convective force

2019 ◽  
Vol 48 (8) ◽  
pp. 3986-3999 ◽  
Author(s):  
B. Ammani Kuttan ◽  
S. Manjunatha ◽  
S. Jayanthi ◽  
B. J. Gireesha
Keyword(s):  
Boundary Layer ◽  
Energy Transfer ◽  
Fluid Flow ◽  
Boundary Layer Region ◽  
Layer Region

Jet Impingement of a Non-Newtonian Fluid

2006 ◽  
Author(s):  
Jiangang Zhao ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Hydraulic Jump ◽  
Similarity Solutions ◽  
Surface Velocity ◽  
Free Surface Velocity ◽  
Viscous Boundary Layer ◽  
Boundary Layer Region ◽  
Layer Region ◽  
Viscous Boundary

The similarity solutions are presented for the wall flow which is formed when a smooth planar jet of power-law fluids impinges vertically on to a horizontal plate, and spreads out in a thin layer bounded by a hydraulic jump. This problem is formulated analogous to radial jet flow problem and the solution procedure is accounted for by means of similarity solution of the boundary-layer equation [1] for Newtonian fluids. For the convenience of analysis, the flow may be divided into three regions, namely a developing boundary-layer region, a fully viscous boundary-layer region, and a hydraulic jump region. The similarity solutions of the film thickness and free surface velocity in fully viscous boundary-layer region include unknown constant L, which is solved numerically and approximately in the developing boundary-layer flow region. Comparison between the numerical and approximate solutions leads generally to good agreement, except for severely shear-thinning fluids. The boundary-layer solution depends on two parameters: power-law index n and α, the dimensionless flow parameters. The effect of α on film thickness and free surface velocity is investigated. The relations between the position of the hydraulic jump and dimensionless flow parameter are obtained and the effect of α on the position of the jump is presented.

scholarly journals Stability of the laminar boundary layer in a streamwise corner

1984 ◽  
Vol 393 (1804) ◽  
pp. 101-116 ◽  
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Viscous Incompressible Flow ◽  
Boundary Layer Region ◽  
Dimensional Boundary ◽  
The Mean ◽  
Layer Region ◽  
The Stability ◽  
Infinite Boundary Value Problem ◽  
Layer Problem

This work examines the stability of viscous, incompressible flow along a streamwise corner, often called the corner boundary-layer problem. The semi-infinite boundary value problem satisfied by small-amplitude disturbances in the ‘blending boundary layer’ region is obtained. The mean secondary flow induced by the corner exhibits a flow reversal in this region. Uniformly valid ‘first approximations’ to solutions of the governing differ­ential equations are derived. Uniformity at infinity is achieved by a suitable choice of the large parameter and use of an appropriate Langer variable. Approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two-dimensional boundary layer profiles.

scholarly journals Transport and Deposition of Large Aspect Ratio Prolate and Oblate Spheroidal Nanoparticles in Cross Flow

Processes ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 886
Author(s):  
Hans O. Åkerstedt
Keyword(s):  
Boundary Layer ◽  
Diffusion Equation ◽  
Convective Diffusion ◽  
Planck Equation ◽  
Deposition Rates ◽  
Fokker Planck Equation ◽  
Analytical Results ◽  
Boundary Layer Region ◽  
Layer Region ◽  
Convective Diffusion Equation

The objective of this paper was to study the transport and deposition of non-spherical oblate and prolate shaped particles for the flow in a tube with a radial suction velocity field, with an application to experiments related to composite manufacturing. The transport of the non- spherical particles is governed by a convective diffusion equation for the probability density function, also called the Fokker–Planck equation, which is a function of the position and orientation angles. The flow is governed by the Stokes equation with an additional radial flow field. The concentration of particles is assumed to be dilute. In the solution of the Fokker–Planck equation, an expansion for small rotational Peclet numbers and large translational Peclet numbers is considered. The solution can be divided into an outer region and two boundary layer regions. The outer boundary layer region is governed by an angle-averaged convective-diffusion equation. The solution in the innermost boundary layer region is a diffusion equation including the radial variation and the orientation angles. Analytical deposition rates are calculated as a function of position along the tube axis. The contribution from the innermost boundary layer called steric- interception deposition is found to be very small. Higher order curvature and suction effects are found to increase deposition. The results are compared with results using a Lagrangian tracking method of the same flow configuration. When compared, the deposition rates are of the same order of magnitude, but the analytical results show a larger variation for different particle sizes. The results are also compared with numerical results, using the angle averaged convective-diffusion equation. The agreement between numerical and analytical results is good.

The boundary layer on a flat plate in a stream with uniform shear

1961 ◽  
Vol 11 (2) ◽  
pp. 309-316 ◽  
Author(s):  
J. D. Murray
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Flat Plate ◽  
Pressure Field ◽  
Free Stream ◽  
Main Stream ◽  
Uniform Shear ◽  
Small Viscosity ◽  
Boundary Layer Region ◽  
Layer Region

The incompressible laminar boundary layer on a semi-infinite flat plate is considered, when the main stream has uniform shear. A solution is obtained for the first two terms of an asymptotic solution for small viscosity. It is shown that one of the principal effects of free-stream vorticity is to introduce a modified pressure field outside the boundary-layer region.

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