Exact solution of the Navier–Stokes equations for the pulsating Dean flow in a channel with porous walls

Tsangaris, S.; Kondaxakis, D.; Vlachakis, N.

doi:10.1016/j.ijengsci.2006.08.010

Cited by 24 publications

(22 citation statements)

References 15 publications

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“…4a-4d that injection has effect of a blowing the graphs away from the wall, since for decreasing s the parameter Λ 1 in the exponential power of Eq. (14) becomes smaller. This is a result of the velocity profiles, obtained in Sect.…”

Section: Heat Conducting Casementioning

confidence: 96%

“…It can be understood from the temperature profiles given by Eq. (14) and Figs. 4a-4d that injection has effect of a blowing the graphs away from the wall, since for decreasing s the parameter Λ 1 in the exponential power of Eq.…”

Section: Heat Conducting Casementioning

confidence: 96%

“…(13) for the injection (s < 0) and zero-suction case, which is given by (14) with the parameters Λ s , α s , β s and Γ s appearing in Eq. (14) defined as…”

Section: Heat Conducting Casementioning

confidence: 99%

“…[13]. Reference [14] found an exact solution for the flow in a porous pipe with unsteady wall suction and/or injection.…”

Section: Introductionmentioning

confidence: 99%

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A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

Türkyılmazoğlu

2012

Acta Mech Sin

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The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow due to a porous disk rotating with a constant angular speed. The three-dimensional hydromagnetic equations of motion are treated analytically to obtained exact solutions with the inclusion of suction and injection. The well-known thinning/thickening flow field effect of the suction/injection is better understood from the constructed closed form velocity equations. Making use of this solution, analytical formulas for the angular velocity components as well as for the permeable wall shear stresses are derived. Interaction of the resolved flow field with the surrounding temperature is further analyzed via the energy equation. The temperature field is shown to accord with the dissipation and the Joule heating. As a result, exact formulas are obtained for the temperature field which take different forms corresponding to the condition of suction or injection imposed on the wall.

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Section: Heat Conducting Casementioning

confidence: 96%

Section: Heat Conducting Casementioning

confidence: 96%

“…(13) for the injection (s < 0) and zero-suction case, which is given by (14) with the parameters Λ s , α s , β s and Γ s appearing in Eq. (14) defined as…”

Section: Heat Conducting Casementioning

confidence: 99%

“…[13]. Reference [14] found an exact solution for the flow in a porous pipe with unsteady wall suction and/or injection.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

Türkyılmazoğlu

2012

Acta Mech Sin

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“…Analytical solutions of equations of motion of a Newtonian fluid for the fully developed laminar flow between the gap of concentric cylinders and the fluid flow is due to the application of oscillating circumferential pressure gradient called finite-gap oscillating Dean flow was considered by Tsangaris et al [22]. Tsangaris and Vlachakis [23] extended the problem to the case where the cylinders walls are porous.…”

Section: Introductionmentioning

confidence: 99%

Transient generalized Taylor-Couette flow: a semi-analytical approach

Jha

Danjuma

2020

Journal of Taibah University for Science

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Semi-analytical solution of transient generalized Taylor-Couette flow of a viscous, incompressible fluid between the gaps of concentric rotating cylinders under applied azimuthal pressure gradient ispresented. The dimensionless governing equations are transformed into standard Bessel equation with the aid of Laplace transformation technique and by a suitable transformation. Analytical solution of the Besselequation is obtained and the Riemann-sum-approximation method of Laplace inversion is utilized. The solution obtained is validated by comparing the Riemann-sum-approximation solution with the exact steady-statesolutions obtained separately. The velocity profile and skin frictions on both surfaces of cylinders are depicted graphically and discussed. The present study reveals that the velocity profile of the fluid is enhanced withincrease in time, and angular velocity,. The velocity profile attains fully developed state at large values of. In addition, increase in pressure gradient, increases the velocity profile of the fluid. Furthermore, back flow occursfor adverse pressure gradient. ARTICLE HISTORY

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Combined effects of suction/injection and exponentially decaying/growing time-dependent pressure gradient on unsteady Dean flow: a semi-analytical approach

Jha

Gambo

2020

Int J Geomath

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Exact solution of the Navier–Stokes equations for the pulsating Dean flow in a channel with porous walls

Cited by 24 publications

References 15 publications

A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

A class of exact solutions for the incompressible viscous magnetohydrodynamic flow over a porous rotating disk

Transient generalized Taylor-Couette flow: a semi-analytical approach

Combined effects of suction/injection and exponentially decaying/growing time-dependent pressure gradient on unsteady Dean flow: a semi-analytical approach

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