IJPAM: Volume 54, No. 2 (2009)

STATIONARY MAGNETIC FLOW OF A SECOND GRADE
FLUID PAST A ROTATING PLANE: EXACT SOLUTIONS

Alessandra Borrelli$^1$, Maria Cristina Patria$^2$
$^{1,2}$Department of Mathematics
University of Ferrara
35, Via Machiavelli, Ferrara, 44100, ITALY
$^1$e-mail: brs@unife.it
$^2$e-mail: pat@unife.it


Abstract.Exact solutions are given for the steady flow of a second grade fluid occupying the halfspace $\mathcal S$ past the plane $z=0$ uniformly rotating about a fixed normal axis ($\equiv z-$axis). No conditions on the sign of the material parameters characterizing the second grade fluid are imposed. The solutions are obtained in a velocity field of the form considered by Berker in [#!Ber!#]. Then a uniform magnetic field ${\bf H}_0$ orthogonal to the (electrically non conducting) rotating plane is impressed. The induced magnetic field is supposed depending only on $z$. The results are compared with those corresponding to the Newtonian case [#!BP!#] and some numerical simulations are given.

Received: June 1, 2009

AMS Subject Classification: 76A05, 76U05, 76W05

Key Words and Phrases: second grade fluids, exact solutions, rotating fluids, magnetohydrodynamics

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 2