Two-Dimensional Stagnation-Point Flow Impinging Obliquely on a Plane Wall

AbstractIn this paper, the steady two-dimensional stagnation-point flow of a viscoelastic Walters’ B’ fluid over a stretching surface is examined. It is assumed that the fluid impinges on the wall obliquely. Using similarity variables, the governing partial differential equations are transformed into a set of two non-dimensional ordinary differential equations. These equations are then solved numerically using the shooting method with a finite-difference technique.

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Unsteady Two-Dimensional Stagnation-Point Flow and Heat Transfer of a Viscous, Compressible Fluid on an Accelerated Flat Plate

Journal of Heat Transfer ◽

10.1115/1.4026008 ◽

2014 ◽

Vol 136 (4) ◽

Cited By ~ 2

Author(s):

H. R. Mozayyeni ◽

Asghar B. Rahimi

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Flat Plate ◽

Ordinary Differential Equations ◽

Stagnation Point ◽

Stagnation Point Flow ◽

Far Field ◽

Two Dimensional ◽

Flow And Heat Transfer ◽

Wide Range

The general formulation and exact solution of the Navier–Stokes and energy equations regarding the problem of steady and unsteady two-dimensional stagnation-point flow and heat transfer is investigated in the vicinity of a flat plate. The plate is moving at time-dependent or constant velocity towards the main low Mach number free stream or away from it. The main stream impinges along z-direction on the flat plate with strain rate a and produces two-dimensional flow. The fluid is assumed to be viscous and compressible. The density of the fluid is affected by the existing temperature difference between the plate and potential far field flow. Suitably introduced similarity transformations are used to reduce the governing equations to a coupled system of ordinary differential equations. Finite Difference Scheme is used to solve these non-linear ordinary differential equations. The obtained results are presented over a wide range of parameters characterizing the problem. It is revealed that the significance of the increase of thermal expansion coefficient, β, and wall temperature on velocity and temperature distributions is much more noticeable for a plate moving away from impinging flow. Moreover, negligible shear stress and heat transfer is reported between the plate and fluid viscous layer close to the plate for a wide range of β coefficient when the plate moves away from incoming far field flow.

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Investigation of Two-Dimensional Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate

Journal of Heat Transfer ◽

10.1115/1.4005742 ◽

2012 ◽

Vol 134 (6) ◽

Cited By ~ 11

Author(s):

Ali Shokrgozar Abbassi ◽

Asghar Baradaran Rahimi

Keyword(s):

Heat Transfer ◽

Strain Rate ◽

Flat Plate ◽

Stagnation Point ◽

Stagnation Point Flow ◽

Navier Stokes ◽

Variable Velocity ◽

Two Dimensional ◽

Flow And Heat Transfer ◽

Energy Equations

General formulation and solution of Navier–Stokes and energy equations are sought in the study of two-dimensional unsteady stagnation-point flow and heat transfer impinging on a flat plate when the plate is moving with variable velocity and acceleration toward main stream or away from it. As an application, among others, this accelerated plate can be assumed as a solidification front which is being formed with variable velocity. An external fluid, along z-direction, with strain rate a impinges on this flat plate and produces an unsteady two-dimensional flow in which the plate moves along z-direction with variable velocity and acceleration in general. A reduction of Navier–Stokes and energy equations is obtained by use of appropriate similarity transformations. Velocity and pressure profiles, boundary layer thickness, and surface stress-tensors along with temperature profiles are presented for different examples of impinging fluid strain rate, selected values of plate velocity, and Prandtl number parameter.

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Unsteady Reversed Stagnation-Point Flow over a Flat Plate

ISRN Applied Mathematics ◽

10.5402/2012/430432 ◽

2012 ◽

Vol 2012 ◽

pp. 1-13 ◽

Cited By ~ 3

Author(s):

Vai Kuong Sin ◽

Chon Kit Chio

Keyword(s):

Laminar Flow ◽

Flow Field ◽

Asymptotic Solution ◽

Stagnation Point ◽

Stokes Equations ◽

Stagnation Point Flow ◽

Navier Stokes ◽

Two Dimensional ◽

Total Flow ◽

Navier Stokes Equations

This paper investigates the nature of the development of two-dimensional laminar flow of an incompressible fluid at the reversed stagnation-point. Proudman and Johnson (1962) first studied the flow and obtained an asymptotic solution by neglecting the viscous terms. Robins and Howarth (1972) stated that this is not true in neglecting the viscous terms within the total flow field. Viscous terms in this analysis are now included, and a similarity solution of two-dimensional reversed stagnation-point flow is investigated by solving the full Navier-Stokes equations.

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Unsteady Stagnation-Point Flow of a Viscoelastic Fluid in the Presence of a Magnetic Field

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2008/573425 ◽

2008 ◽

Vol 2008 ◽

pp. 1-15

Author(s):

F. Labropulu

Keyword(s):

Magnetic Field ◽

Stagnation Point ◽

Infinite Plate ◽

Transverse Magnetic ◽

Weissenberg Number ◽

Stagnation Point Flow ◽

Two Dimensional ◽

Harmonic Oscillations ◽

Finite Difference Technique ◽

Walters B Fluid

The unsteady two-dimensional stagnation point flow of the Walters B' fluid impinging on an infinite plate in the presence of a transverse magnetic field is examined and solutions are obtained. It is assumed that the infinite plate aty=0is making harmonic oscillations in its own plane. A finite difference technique is employed and solutions for small and large frequencies of the oscillations are obtained for various values of the Hartmann's number and the Weissenberg number.

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