scholarly journals Ferromagnetic Flow of Viscous Fluid in a Slot between Fixed Surfaces of Revolution

2016 ◽  
Vol 23 (4) ◽  
pp. 99-104 ◽  
Author(s):  
Sawicki Jerzy
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Viscous Fluid ◽  
Coordinate System ◽  
Axial Symmetry ◽  
Surfaces Of Revolution ◽  
Orthogonal Coordinate System ◽  
Boundary Layer Equations ◽  
Axis Of Symmetry ◽  
Steady Laminar

Abstract In this paper the steady laminar flow of viscous incompressible ferromagnetic fluid is considered in a slot between fixed surfaces of revolution having a common axis of symmetry. The boundary layer ferromagnetic equations for axial symmetry are expressed in terms of the intrinsic curvilinear orthogonal coordinate system x, θ ,y.The method of perturbation is used to solve the boundary layer equations. As a result, the formulae defining such parameters of the flow as the velocity components vx, vy, and the pressure , were obtained.

The heated laminar vertical jet

1967 ◽  
Vol 29 (2) ◽  
pp. 305-315 ◽  
Author(s):  
R. S. Brand ◽  
F. J. Lahey
Keyword(s):  
Boundary Layer ◽  
Temperature Distribution ◽  
Laminar Flow ◽  
Prandtl Number ◽  
Exact Solutions ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Prandtl Numbers ◽  
Vertical Jet ◽  
Steady Laminar

The boundary-layer equations for the steady laminar flow of a vertical jet, including a buoyancy term caused by temperature differences, are solved by similarity methods. Two-dimensional and axisymmetric jets are treated. Exact solutions in closed form are found for certain values of the Prandtl number, and the velocity and temperature distribution for other Prandtl numbers are found by numerical integration.

A Fast Approximate Solution of the Laminar Boundary-Layer Equations

1986 ◽  
Vol 108 (2) ◽  
pp. 200-207 ◽  
Author(s):  
Sei-ichi Iida ◽  
Akira Fujimoto
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Computational Time ◽  
Computational Techniques ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Layer Characteristic ◽  
Comparison Of The Results ◽  
Steady Laminar

A new approximate method of calculating steady laminar boundary-layers is presented. This method is based on the mutual relationships between boundary-layer characteristic quantities. The governing equations are efficiently solved without assuming a specific velocity profile. Moreover, a method of estimating the velocity profile using the characteristic quantities is also proposed. Comparison of the results obtained for a wide variety of applications to boundary-layer flows with separations with exact solutions indicates that the present method enables one to obtain solutions with sufficient accuracy and shorter computational time when compared with existing computational techniques.

scholarly journals Planar flows past thin multi-blade configurations

1996 ◽  
Vol 324 ◽  
pp. 355-377 ◽  
Author(s):  
F. T. Smith ◽  
S. N. Timoshin
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Laminar Flows ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Require Solution ◽  
Lift And Drag ◽  
Planar Flows ◽  
Steady Laminar

Two-dimensional steady laminar flows past multiple thin blades positioned in near or exact sequence are examined for large Reynolds numbers. Symmetric configurations require solution of the boundary-layer equations alone, in parabolic fashion, over the successive blades. Non-symmetric configurations in contrast yield a new global inner–outer interaction in which the boundary layers, the wakes and the potential flow outside have to be determined together, to satisfy pressure-continuity conditions along each successive gap or wake. A robust computational scheme is used to obtain numerical solutions in direct or design mode, followed by analysis. Among other extremes, many-blade analysis shows a double viscous structure downstream with two streamwise length scales operating there. Lift and drag are also considered. Another new global interaction is found further downstream. All the interactions involved seem peculiar to multi-blade flows.

Transformations of the boundary-layer equations for rotating flows

1968 ◽  
Vol 33 (1) ◽  
pp. 113-126
Author(s):  
N. Rott ◽  
J. T. Ohrenberger
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Compressible Flow ◽  
Incompressible Flow ◽  
Flow Problem ◽  
Rotating Flows ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Axis Of Symmetry ◽  
Semi Empirical

The boundary layer on an axisymmetric surface above which the flow is rotating about the axis of symmetry is considered. Transformations of the governing equations which permit the generalizations of a known solution for one meridian shape in incompressible flow to a family of meridian shapes are shown to exist. For compressible flow, a transformation of the Stewartson-Illingworth type was found which reduces a compressible flow problem to an incompressible case. Also, remarks are made concerning the invariance of the turbulent boundary-layer integral equations assuming particular semi-empirical shear laws.

Singularities in solutions of the three-dimensional laminar-boundary-layer equations

1985 ◽  
Vol 160 ◽  
pp. 257-279 ◽  
Author(s):  
James C. Williams
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Unsteady Boundary Layer ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
New Type ◽  
Steady Laminar

The three-dimensional steady laminar-boundary-layer equations have been cast in the appropriate form for semisimilar solutions, and it is shown that in this form they have the same structure as the semisimilar form of the two-dimensional unsteady laminar-boundary-layer equations. This similarity suggests that there may be a new type of singularity in solutions to the three-dimensional equations: a singularity that is the counterpart of the Stewartson singularity in certain solutions to the unsteady boundary-layer equations.A family of simple three-dimensional laminar boundary-layer flows has been devised and numerical solutions for the development of these flows have been obtained in an effort to discover and investigate the new singularity. The numerical results do indeed indicate the existence of such a singularity. A study of the flow approaching the singularity indicates that the singularity is associated with the domain of influence of the flow for given initial (upstream) conditions as is prescribed by the Raetz influence principle.

Laminar Flow Along a Porous Vertical Wall

1982 ◽  
Vol 49 (1) ◽  
pp. 250-253 ◽  
Author(s):  
P. D. Verma ◽  
K. C. Sarangi ◽  
P. D. Ariel
Keyword(s):  
Boundary Layer ◽  
Integral Equation ◽  
Laminar Flow ◽  
Film Thickness ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Dimensionless Parameter ◽  
Vertical Wall ◽  
Suction Parameter ◽  
Steady Laminar

The behavior of boundary layer thickness, film thickness is investigated for steady laminar flow along a porous vertical wall. Using a sixth-degree velocity profile the resulting equation from the Von Karman integral equation has been integrated numerically. The boundary layer thickness, film thickness are shown graphically for different values of suction parameter λ1 = v0h0/ν and a dimensionless parameter φ=3νu0gh021/2.

Axially invariant laminar flow in helical pipes with a finite pitch

1993 ◽  
Vol 251 ◽  
pp. 315-353 ◽  
Author(s):  
Shijie Liu ◽  
Jacob H. Masliyah
Keyword(s):  
Laminar Flow ◽  
Coordinate System ◽  
Secondary Flow ◽  
Flow Pattern ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Helical Flow ◽  
The Body ◽  
Dean Number ◽  
Orthogonal Coordinate System

Steady axially invariant (fully developed) incompressible laminar flow of a Newtonian fluid in helical pipes of constant circular cross-section with arbitrary pitch and arbitrary radius of coil is studied. A loose-coiling analysis leads to two dominant parameters, namely Dean number, Dn = Reλ½, and Germano number, Gn = Reη, where Re is the Reynolds number, λ is the normalized curvature ratio and η is the normalized torsion. The Germano number is embedded in the body-centred azimuthal velocity which appears as a group in the governing equations. When studying Gn effects on the helical flow in terms of the secondary flow pattern or the secondary flow structure viewed in the generic (non-orthogonal) coordinate system of large Dn, a third dimensionless group emerges, γ = η/(λDn)½. For Dn < 20, the group γ* = Gn Dn-2 = η/(λRe) takes the place of γ.Numerical simulations with the full Navier-Stokes equations confirmed the theoretical findings. It is revealed that the effect of torsion on the helical flow can be neglected when γ ≤ 0.01 for moderate Dn. The critical value for which the secondary flow pattern changes from two vortices to one vortex is γ* > 0.039 for Dn < 20 and γ > 0.2 for Dn ≥ 20. For flows with fixed high Dean number and A, increasing the torsion has the effect of changing the relative position of the secondary flow vortices and the eventual formation of a flow having a Poiseuille-type axial velocity with a superimposed swirling flow. In the orthogonal coordinate system, however, the secondary flow generally has two vortices with sources and sinks. In the small-γ limit or when Dn is very small, the secondary flow is of the usual two-vortex type when viewed in the orthogonal coordinate system. In the large-γ limit, the appearance of the secondary flow in the orthogonal coordinate system is also two-vortex like but its orientation is inclined towards the upper wall. The flow friction factor is correlated to account for Dn, A and γ effects for Dn ≤ 5000 and γ < 0.1.

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