The Flow of an Elastico-Viscous Liquid between Two Electrically Non-Conducting Infinite Flat Plates under a Uniform Transverse Magnetic Field

Abstract

Flow of a visco-elastic fluid near an oscillating plate and between two plates oscillating with a phase difference, with the same frequency and different amplitudes, under a transverse magnetic field fixed relative to the fluid and fixed relative to one of the plates has been considered employing a well known simple complex variable technique. Expressions for velocity profile, the induced magnetic field and the shear stresses on the plates in all the situations have been calculated exactly as well as approximately in the two limiting cases of small and large values of the Reynolds number. In the case of two oscillating plates, the skin friction on the two plates tend to the same value in the limiting case when the Reynolds number tends to zero. The shearing stress on the lower plate, in the limiting case when the Reynolds number tends to infinity, behaves as if the other plate were absent. These results hold whether the magnetic lines of force are fixed relative to the fluid or to one of the plates.