## Journal of Geometry and Symmetry in Physics

### Unsteady Roto-Translational Viscous Flow: Analytical Solution to Navier-Stokes Equations in Cylindrical Geometry

#### Abstract

We study the unsteady viscous flow of an incompressible, isothermal (Newtonian) fluid whose motion is induced by the sudden swirling of a cylindrical wall and is also starting with an axial velocity component. Basic physical assumptions are that the pressure axial gradient keeps its hydrostatic value and the radial velocity is zero. In such a way the Navier-Stokes PDEs become uncoupled and can be solved separately. Accordingly, we provide analytic solutions to the unsteady speed components, i.e., the axial $v_z(r,t)$ and the circumferential $v_\theta(r,t)$, by means of expansions of Fourier-Bessel type under time damping. We also find: the surfaces of dynamical equilibrium, the wall shear stress during time and the Stokes streamlines.

#### Article information

Source
J. Geom. Symmetry Phys., Volume 48 (2018), 1-21.

Dates
First available in Project Euclid: 24 May 2018

https://projecteuclid.org/euclid.jgsp/1527127300

Digital Object Identifier
doi:10.7546/jgsp-48-2018-1-21

Mathematical Reviews number (MathSciNet)
MR3822797

Zentralblatt MATH identifier
06944469

#### Citation

Bocci, Alessio; Scarpello, Giovanni Mingari; Ritelli, Daniele. Unsteady Roto-Translational Viscous Flow: Analytical Solution to Navier-Stokes Equations in Cylindrical Geometry. J. Geom. Symmetry Phys. 48 (2018), 1--21. doi:10.7546/jgsp-48-2018-1-21. https://projecteuclid.org/euclid.jgsp/1527127300