biomaths, k.k.jain colleg khatauli,muzaffarnagar
Mathematics, D.A.V. (PG) College
This paper deals with the theoretical investigation of the thermal instability of a thin layer of electrically conducting micropolar rotating fluid, heated from below in the presence of uniform vertical magnetic field in porous medium. A dispersion relation is obtained for a flat fluid layer, contained between two free boundaries using a linear stability analysis theory, and normal mode analysis method. The principle of Exchange of Stabilities (PES) is found to hold true for the micropolar fluid saturating a porous medium, heated from below in the absence of magnetic field, rotation and coupling between thermal and micropolar effects. It is also found that PES is valid in the presence of rotation and magnetic field under certain conditions. The oscillatory modes are introduced due to the presence of magnetic field and rotation, which were non-existence in their absence. The presence of coupling between thermal and micropolar effects may also introduce oscillatory modes. For the case of stationary convection, the effect of various parameters like medium permeability, rotation, magnetic field (in the presence and absence of micropolar heat conduction parameter), coupling parameter, micropolar coefficient and micropolar heat conduction parameter has been analyzed and results are depicted graphically. The sufficient conditions for the non-existence of overstability are also obtained. In this paper, an attempt is also made to apply the variational principle for the present problem and found that the said principle can be established for the present problem in the absence of coupling between spin and heat flux.