Flow and Mass Transfer for an Unsteady Stagnation-Point Flow Over a Moving Wall Considering Blowing Effects

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
Tiegang Fang
Keyword(s):  
Mass Transfer ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Local Maximum ◽  
Wall Stress ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Mass Transfer Equation ◽  
Moving Wall

In this paper, the flow and mass transfer of a two-dimensional unsteady stagnation-point flow over a moving wall, considering the coupled blowing effect from mass transfer, is studied. Similarity equations are derived and solved in a closed form. The flow solution is an exact solution to the two-dimensional unsteady Navier–Stokes equations. An analytical solution of the boundary layer mass transfer equation is obtained together with the momentum solution. The examples demonstrate the significant impacts of the blowing effects on the flow and mass transfer characteristics. A higher blowing parameter results in a lower wall stress and thicker boundary layers with less mass transfer flux at the wall. The higher wall moving parameters produce higher mass transfer flux and blowing velocity. The Schmidt parameters generate a local maximum for the mass transfer flux and blowing velocity under given wall moving and blowing parameters.

scholarly journals Unsteady Reversed Stagnation-Point Flow over a Flat Plate

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
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.

Oscillating stagnation point flow

1982 ◽  
Vol 384 (1786) ◽  
pp. 175-190 ◽  
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
High Frequency ◽  
Stokes Equations ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Analytic Approximations ◽  
Numerical Integrations ◽  
Hiemenz Flow

A solution of the Navier-Stokes equations is given for an incompressible stagnation point flow whose magnitude oscillates in time about a constant, non-zero, value (an unsteady Hiemenz flow). Analytic approximations to the solution in the low and high frequency limits are given and compared with the results of numerical integrations. The application of these results to one aspect of the boundary layer receptivity problem is also discussed.

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

2012 ◽  
Vol 134 (6) ◽  
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.

Nonaxisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Ali Shokrgozar Abbassi ◽  
Asghar Baradaran Rahimi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flat Plate ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Dimensional Flow ◽  
Flow And Heat Transfer

The existing solutions of Navier–Stokes and energy equations in the literature regarding the three-dimensional problem of stagnation-point flow either on a flat plate or on a cylinder are only for the case of axisymmetric formulation. The only exception is the study of three-dimensional stagnation-point flow on a flat plate by Howarth (1951, “The Boundary Layer in Three-Dimensional Flow—Part II: The Flow Near Stagnation Point,” Philos. Mag., 42, pp. 1433–1440), which is based on boundary layer theory approximation and zero pressure assumption in direction of normal to the surface. In our study the nonaxisymmetric three-dimensional steady viscous stagnation-point flow and heat transfer in the vicinity of a flat plate are investigated based on potential flow theory, which is the most general solution. An external fluid, along z-direction, with strain rate a impinges on this flat plate and produces a two-dimensional flow with different components of velocity on the plate. This situation may happen if the flow pattern on the plate is bounded from both sides in one of the directions, for example x-axis, because of any physical limitation. A similarity solution of the Navier–Stokes equations and energy equation is presented in this problem. A reduction in these equations is obtained by the use of appropriate similarity transformations. Velocity profiles and surface stress-tensors and temperature profiles along with pressure profile are presented for different values of velocity ratios, and Prandtl number.

Blow-up of unsteady two-dimensional Euler and Navier-Stokes solutions having stagnation-point form

1989 ◽  
Vol 203 ◽  
pp. 1-22 ◽  
Author(s):  
S. Childress ◽  
G. R. Ierley ◽  
E. A. Spiegel ◽  
W. R. Young
Keyword(s):  
Stagnation Point ◽  
Blow Up ◽  
Stokes Equations ◽  
Point Vortex ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Infinite Domain ◽  
Initial Vorticity ◽  
Point Form

The time-dependent form of the classic, two-dimensional stagnation-point solution of the Navier-Stokes equations is considered. If the viscosity is zero, a class of solutions of the initial-value problem can be found in closed form using Lagrangian coordinates. These solutions exhibit singular behaviour in finite time, because of the infinite domain and unbounded initial vorticity. Thus, the blow-up found by Stuart in three dimensions using the stagnation-point form, also occurs in two. The singularity vanishes under a discrete, finite-dimensional ‘point vortex’ approximation, but is recovered as the number of vortices tends to infinity. We find that a small positive viscosity does not arrest the breakdown, but does strongly alter its form. Similar results are summarized for certain Boussinesq stratified flows.

Similarity solutions for unsteady stagnation point flow

2012 ◽  
Vol 711 ◽  
pp. 394-410 ◽  
Author(s):  
D. Kolomenskiy ◽  
H. K. Moffatt
Keyword(s):  
Stagnation Point ◽  
Stokes Equations ◽  
Nonlinear Ordinary Differential Equation ◽  
Similarity Solutions ◽  
Parameter Family ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Plane Boundary ◽  
Wide Range ◽  
Flow Situation

AbstractA class of similarity solutions for two-dimensional unsteady flow in the neighbourhood of a front or rear stagnation point on a plane boundary is considered, and a wide range of possible behaviour is revealed, depending on whether the flow in the far field is accelerating or decelerating. The solutions, when they exist, are exact solutions of the Navier–Stokes equations, having a boundary-layer character analogous to that of the classical steady front stagnation point flow. The velocity profiles are obtained by numerical integration of a nonlinear ordinary differential equation. For the front-flow situation, the solution is unique for the accelerating case, but bifurcates for modest deceleration, while for sufficient rapid deceleration there exists a one-parameter family of solutions. For the rear-flow situation, a unique solution exists (remarkably!) for sufficiently strong acceleration, and a one-parameter family again exists for sufficient strong deceleration. Analytic results, which are consistent with the numerical results, are obtained in the limits of strong acceleration or deceleration, and for the asymptotic behaviour far from the boundary.

scholarly journals On a class of unsteady three-dimensional Navier—Stokes solutions relevant to rotating disc flows: threshold amplitudes and finite-time singularities

1992 ◽  
Vol 238 ◽  
pp. 297-323 ◽  
Author(s):  
Philip Hall ◽  
P. Balakumar ◽  
D. Papageorgiu
Keyword(s):  
Exact Solution ◽  
Velocity Field ◽  
Continuous Spectrum ◽  
Stagnation Point ◽  
Finite Time ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Stagnation Point Flow ◽  
Navier Stokes ◽  
Rotating Disc

A class of ‘exact’ steady and unsteady solutions of the Navier—Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating in the (x, y)-plane with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x, — y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large Kármán's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation-point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Kármán's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite-time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial-value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.

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