Boundary Layer Flow About and Inside a Liquid Sphere

1997 ◽  
Vol 119 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Maged A. I. El-Shaarawi ◽  
Abdulghani Al-Farayedhi ◽  
Mohamed A. Antar
Keyword(s):  
Boundary Layer ◽  
Solid Sphere ◽  
External Flow ◽  
Droplet Surface ◽  
Laminar Flows ◽  
Surface Velocity ◽  
Immiscible Fluid ◽  
Interface Shear ◽  
Boundary Layer Equations ◽  
Layer Flow

A finite-difference scheme has been developed to solve the boundary-layer equations governing laminar flows around and inside a spherical fluid droplet moving steadily in another immiscible fluid. Using this scheme, results not available in the literature have been obtained for circulating droplets at intermediate and high interior-to-exterior viscosity ratios (μ*) and large values of the external flow Reynolds number (Re). Detailed results over the range 1.01 ≤ μ* ≤ ∞ (solid sphere) and 100 ≤ Re ≤ 10000 are presented for the velocity profiles outside and inside the droplet, the interface shear stress, the external flow separation angle, the droplet surface velocity and the drag coefficient.

scholarly journals Numerical method approach for magnetohydrodynamic radiative ferrofluid flows over a solid sphere surface

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 379-385
Author(s):  
Yasin Mat ◽  
Muhammad Mohamed ◽  
Zulkhibri Ismail ◽  
Basuki Widodo ◽  
Mohd Salleh
Keyword(s):  
Boundary Layer ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Solid Sphere ◽  
Skin Friction Coefficient ◽  
Fluid Temperature ◽  
Sphere Surface ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Layer Flow

In this paper, the theoretical study on the laminar boundary-layer flow of ferrofluid with influences of magnetic field and thermal radiation is investigated. The viscosity of ferrofluid flow over a solid sphere surface is examined theoretically for magnetite volume fraction by using boundary-layer equations. The governing equations are derived by applied the non-similarity transformation then solved numerically by utilizing the Keller-box method. It is found that the increments in ferro-particles (Fe3O4) volume fraction declines the fluid velocity but elevates the fluid temperature at a sphere surface. Consequently, the results showed viscosity is enhanced with the increase of the ferroparticles volume fraction and acts as a pivotal role in the distribution of velocity, temperature, reduced skin friction coefficient, and reduced Nusselt number of ferrofluid.

Dual solutions of the boundary-layer equations at a point of attachment

1967 ◽  
Vol 30 (4) ◽  
pp. 809-811 ◽  
Author(s):  
D. Schofield ◽  
A. Davey
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Nodal Point ◽  
External Flow ◽  
Dual Solutions ◽  
Dual Solution ◽  
Boundary Layer Equations ◽  
Layer Flow

This paper indicates the existence of a dual solution of the boundary-layer equations for the flow near a nodal point of attachment of the external flow; especial note is made of the non-axisymmetric boundary-layer flow when the external flow is axisymmetric.

Boundary-Layer Flow Between the Attachment Lines on a Flat Plate Delta Wing at Incidence

1962 ◽  
Vol 13 (1) ◽  
pp. 1-16
Author(s):  
J. C. Cooke
Keyword(s):  
Boundary Layer ◽  
Delta Wing ◽  
Three Dimensional ◽  
External Flow ◽  
Two Dimensional ◽  
Conical Flow ◽  
Slender Body Theory ◽  
Layer Flow ◽  
Body Theory ◽  
Transition Fronts

SummaryA three-dimensional laminar-boundary-layer calculation is carried out over the area concerned. The external flow is simplified, being calculated by slender-body theory assuming conical flow, with two point vortices above the wing, their positions and strength being determined by experiment. Attempts are made to draw transition fronts both for two-dimensional and sweep instability from this calculation. The combination of these gives fronts similar to those observed in some experiments. Because there is little or no pressure gradient over the area in question it is suggested that it is a region where distributed suction might usefully be applied in order to maintain laminar flow and reduce drag.

scholarly journals Separation Points of Magneto-hydrodynamic Boundary Layer Flow Along a Vertical Plate with Exponentially Decreasing Free Stream Velocity

1970 ◽  
Vol 5 (1) ◽  
pp. 11-18 ◽  
Author(s):  
MA Alim ◽  
MM Rahman ◽  
MM Karim
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Vertical Plate ◽  
Free Stream ◽  
Stream Velocity ◽  
Convection Boundary Layer ◽  
Boundary Layer Equations ◽  
Box Scheme ◽  
Convection Boundary ◽  
Layer Flow

The points of separation of magneto-hydrodynamic mixed convection boundary layer flow along a vertical plate have been investigated. The free stream velocity is considered decreasing exponentially in the stream wise direction. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations are reduced to local non-similar boundary layer equations, which are solved numerically by implicit finite difference method known as Keller box scheme. Here we have focused our attention to find the effects of suction, magnetic field and other relevant physical parameters on the position of boundary layer separation. The numerical results are expressed in terms of local shear stress showing the effects of suction, buoyancy, Prandlt number and magnetic field on the shear stress as well as on the points of separation. Keywords: Separation points, magneto-hydrodynamic, mixed convection, boundary layer, suction, finite difference method, Keller box scheme.   doi:10.3329/jname.v5i1.1868Journal of Naval Architecture and Marine Engineering Vol. 5, No. 1 (June, 2008) 11-18. 

Spreadsheets Solutions of the Boundary Layer Equations

2004 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Fluid Mechanics ◽  
Undergraduate Students ◽  
Classical Problem ◽  
Boundary Layer Equations ◽  
Specialized Software ◽  
Layer Flow ◽  
Basic Course ◽  
The Impact

A classical problem in fluid mechanics and heat transfer is boundary layer flow over a flat plate. This problem is used to demonstrate a number of important concepts in fluid mechanics and heat transfer. Typically, in a basic course, the equations are derived and the solutions are presented in tabular or chart from. Obtaining the actual solutions is mathematically and numerically too involved to be covered in basic courses. In this paper, it is shown that the similarity solution and the solution to boundary layer equations in the primitive variables can easily be obtained using spreadsheets. Without needing much programming skills, or needing to learn specialized software, undergraduate students can use this approach and obtain the solution and study the impact of different parameters.

Three-Dimensional Boundary-Layer Flow About an Ablating Slender Cone

1969 ◽  
Vol 91 (4) ◽  
pp. 632-648 ◽  
Author(s):  
T. K. Fannelop ◽  
P. C. Smith
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Cone Angle ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Boundary Layer Equations ◽  
Transverse Curvature ◽  
Dimensional Boundary ◽  
Layer Flow

A theoretical analysis is presented for three-dimensional laminar boundary-layer flow about slender conical vehicles including the effect of transverse surface curvature. The boundary-layer equations are solved by standard finite difference techniques. Numerical results are presented for hypersonic flow about a slender blunted cone. The influences of Reynolds number, cone angle, and mass transfer are studied for both symmetric flight and at angle-of-attack. The effects of transverse curvature are substantial at the low Reynolds numbers considered and are enhanced by blowing. The crossflow wall shear is largely unaffected by transverse curvature although the peak velocity is reduced. A simplified “channel flow” analogy is suggested for the crossflow near the wall.

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.

On three-dimensional boundary layer flow over surface irregularities

1980 ◽  
Vol 373 (1754) ◽  
pp. 311-329 ◽  
Keyword(s):  
Boundary Layer ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Solution Technique ◽  
Parabolic Boundary ◽  
Boundary Layer Equations ◽  
Surface Irregularities ◽  
Dimensional Boundary ◽  
Layer Flow

The three-dimensional pipeflow boundary layer equations of Smith (1976) are shown to apply to certain external flow problems, and a numerical method for their solution is developed. The method is used to study flow over surface irregularities, and some three-dimensional separated flows are calculated. Upstream influence in the form of so-called ‘free interactions’ requires an iterative solution technique, in which the initial conditions for the parabolic boundary layer equations must be determined to satisfy a downstream condition

The Laminar Boundary Layer on a Hot Cylinder Fixed in a Fluctuating Stream

1961 ◽  
Vol 28 (3) ◽  
pp. 339-346 ◽  
Author(s):  
R. J. Gribben
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Laminar Boundary Layer ◽  
Small Amplitude ◽  
External Flow ◽  
Low Speed ◽  
Boundary Layer Equations ◽  
Special Cases ◽  
Exact Calculations ◽  
Small Amplitude Oscillation

The equations for nonsteady, two-dimensional low-speed compressible flow in the laminar boundary layer are solved approximately by use of the Pohlhausen technique with the assumption of quartic profiles for the velocity and temperature. The external flow considered is of the form of a steady basic velocity with a superimposed small amplitude oscillation such as may arise, for example, when a sound wave is present in a uniform incident stream. The analysis is then applicable to the case of a hot cylinder fixed in such a stream. Terms of the order of the incident stream Mach number are neglected in the expressions for external flow quantities (whereas the low-speed boundary-layer equations involve errors of the order of only the square of this Mach number). Two special cases are worked out—the flow over a flat plate for which there is fair agreement with available exact calculations, and the flow over a circular cylinder.

Sign in / Sign up

Export Citation Format

Share Document