Flows for chosen vorticity functions exact solutions of the Navier‐Stokes equations

Chandna, O. P.; Oku-Ukpong, E. O.

doi:10.1155/s0161171294000219

Cited by 18 publications

(18 citation statements)

References 4 publications

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“…The complex mathematical structure of NSE offers a great difficulty in achieving exact solutions; however, we find some transformation techniques and dimension analysis method that were helpful in providing some new exact solutions. We refer here [1][2][3][4][5][6][7][8][9][10][11][12][13] and reference therein for some exact solutions of NSE with surface forces on right-hand side of NSE using a variety of techniques/methods, however [14] considered NSE with coriolis force and [15] gave a basic remark on NSE with body force. We further mention here some attempts to the problem of finding exact solutions of the equations describing the steady plane flows of incompressible fluid of variable viscosity in the presence of body force.…”

Section: Introductionmentioning

confidence: 99%

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A Class of New Exact Solutions of Navier-Stokes Equations with Body Force For Viscous Incompressible Fluid

Ahmed

Naeem

Ali

2018

IJAMR

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This paper is to indicate a class of new exact solutions of the equations governing the two-dimensional steady motion of incompressible fluid of variable viscosity in the presence of body force. The class consists of the stream function $\psi$ characterized by equation $\theta=f(r)+ a \psi + b $ in polar coordinates $r$, $\theta$ , where a continuously differentiable function is $f(r)$ and $a\neq 0 , b $ are constants. The exact solutions are determined for given one component of the body force, for both the cases when $f(r)$ is arbitrary and when it is not. When $f(r)$ is arbitrary, we find $a=1$ and we can construct an infinite set of streamlines and the velocity components, viscosity function, generalized energy function and temperature distribution for the cases when $R_{e}P_{r}=1$ and when $R_{e}P_{r}\neq 1$ where $R_{e}$ represents Reynolds number and $P_{r}$Prandtl number. For the case when $f(r)$ is not arbitrary we can find solutions for the cases $R_{e}P_{r}\neq a$ and $R_{e}P_{r}=a$ where $"a"$ remains arbitrary.

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Section: Introductionmentioning

confidence: 99%

“…Experience shows that the exact solution of equations (4-6 ) offers a great difficulty because of the presence of the non-linear term, therefore we write equation (4)(5)(6) in following manage able form by introducing the vorticity function w and the total energy function L defined by…”

Section: Introductionmentioning

confidence: 99%

A Class of New Exact Solutions of Navier-Stokes Equations with Body Force For Viscous Incompressible Fluid

Ahmed

Naeem

Ali

2018

IJAMR

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“…However, because of substantial nonlinearity of these equations, only a small number of exact solutions to them were found [5][6][7][8][9][10]. Our aim is to obtain some new exact solutions to the Navier-Stokes equations that could have interesting applications.…”

Section: Introductionmentioning

confidence: 99%

On axially symmetric solutions of the Navier-Stokes equations

Rabinowitch

2013

International Journal of Advanced Mathematical Sciences

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In the present paper, the Navier-Stokes equations are studied in several axially symmetric cases. In them incompressible viscous fluids rotate about their axes and can change their shape. In the considered cases, three exact solutions to the Navier-Stokes equations are found. The first of these solutions describes rotating viscous fluids that are gradually cooling. The second of them describes nonstationary rotations with axial motions of viscous fluids. The third of the obtained solutions to the Navier-Stokes equations concerns rotating viscous fluids with stationary velocities. It is used to describe the observable phenomenon of differential rotation of the visible surfaces of stars and giant gas planets.

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“…Following the Martin's formulation (Martin, M.H., 1971), some researchers (Chandna, O.P., et al, 1982;Siddiqui, A.M., et al, 2008) have used hodograph transformation (Ames, W.F., et al, 1965) in order to linearized the system of governing equations and successfully got some exact solutions. Some authors (Chandna, O.P., et al, 1994;Hayat, T., et al, 1988 ) have used inverse method (Nemenyi, 1951) where some a priori condition is assumed about the flow variables and have found some exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Some Exact Solutions of Plane Steady Hydromagnetic Flow with Variable Viscosity

Мишра¹,

Mishra²,

Srivastava³

2011

JMR

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Flows for chosen vorticity functions exact solutions of the Navier‐Stokes equations

Abstract: ABSTRACT. Solutions are obtained for the equations of the motion of the steady incompressible viscous planar generalized Beltrami flows when the vorticity distribution is given by V2b + f(z,y) for three chosen forms of f(z,).

Cited by 18 publications

References 4 publications

A Class of New Exact Solutions of Navier-Stokes Equations with Body Force For Viscous Incompressible Fluid

A Class of New Exact Solutions of Navier-Stokes Equations with Body Force For Viscous Incompressible Fluid

On axially symmetric solutions of the Navier-Stokes equations

Some Exact Solutions of Plane Steady Hydromagnetic Flow with Variable Viscosity

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