2016/09/17 by Alessio Bocci, Bocci, Alessio, Giovanni Mingari Scarpello +3
Chemical Engineering · Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.1609.05392
openalex publication_date 2016/09/17 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28
We provide a integration of Navier-Stokes equations concerning the unsteady-state laminar flow of an incompressible, isothermal (newtonian) fluid in a cylindrical vessel spinning about its symmetry axis, say z, and inside which the liquid velocity starts with a non-zero axial component as well. Basic physical assumptions are that the pressure axial gradient keeps itself on its hydrostatic value and that no radial velocity exists. In such a way the PDEs become uncoupled and can be faced separately from each other. We succeed in computing both the unsteady velocities, i.e. the axial vz and the circumferential vθ as well, by means of infinite series expansions of Fourier-Bessel type under time exponential damping. Following this, we also find the unsteady surfaces of dynamical equilibrium, the wall shear stress and the Stokesian streamlines