भौतिक गणित

Wave Perturbations for Linear Instability of Magneto Hydrodynamic Hartman Flow between Parallel Plates

Abstract

Zakir Hussain, Huisheng Zhang and Sergei Zuev

The Hartmann layers of conducting fluid between parallel plates under the influence of the transvers magnetic field are considered. The standard boundary conditions with zero velocities on the plates are used. The perturbations are used to obtain the exact solution for the given system. It is shown explicitly that no instability near the stationary solution can be found by perturbations in 2-dim cases. In 3-dim case the instability arises just when quaternionic perturbations applied. We use analytical solutions to obtain explicit results and wave perturbations for considered system. Our results are agreed with experimental facts which was solved by other authors and confirms the wellknown fact that traversal magnetic field overcomes the instability. Similarly we obtained the exact solution by using new quaternionic method and this way of nonlinear system consideration can deliver a variety of possibilities for finding new solutions.