THERMAL INSTABILITY OF A ROTATING MHD MICROPOLAR FLUID LAYER HEATED FROM BLOW SATURATING A POROUS MEDIUM Bhupander Singh, Associate Professor, Department of Mathematics, Meerut College, Meerut U.P. INDIA-25ooo1 Abstract A theoretical investigation of thermal instability of an electrically non-conducting, incompressible, rotating micropolar fluid layer heated from blow saturating a porous medium in the presence of magnetic field is worked out. Using linear stability analysis theory and normal mode technique a dispersion relation is obtained for a flat fluid layer confined between two free boundaries . The variation of thermal Rayleigh number with recpect to the variation of various parameters like medium permeability, rotation, coupling parameter, magnetic field and micropolar heat conduction parameter are predicted their nature on the onset of stationary convection and results are depicted graphically. The principle of exchange of stability (PES) is found valid. The sufficient condition for the existence of overstability is also obtained. Keywords: Thermal Instability; Micropolar Fluid; Magnetic Field; Rotation; Porous Medium 1. INTRODUCTION Thermal effects in microfluids discussed by Eringen[1] and Kazakia et. al[9]. Sastry and Rao[8] discussed the stability of a hot rotating micropolar fluid layer between two rigid boundaries without taking into account the rotation effect in the angular momentum equation. On the other hand Bhattacharyya and Abbas[7] took into account the rotation effect in both momentum equations with free boundaries. Sastry and Rao[8] noticed that when the fluid is heated from below, the rotation of the system delays the onset of stability. Y. Qin and P.N. Kaloni[10] studied the effect of rotation on thermal convection in micropolar fluid and found that the effect of rotation in a stationary convection is stabilizing and that higher the values of the micropolar parameters, the more the stabilizing effect. For over-stability to be possible, r P (Prandtl number) must be less than 1 / (1 ) k + , where k is a coupling parameter. Sharma and Kumar[2] studied the effect of rotation on thermal convection in micropolar fluid in non- porous medium and found that the presence of coupling between thermal and micropolar effects and uniform rotation may introduce oscillatory modes in the system. Sharma and Kumar[3] studied the effect of rotation on thermal convection in micropolar fluid in porous medium and found that the presence of rotation and coupling between spin and heat fluxes may bring over-stability in the system and the medium permeability also brings in over-stability in the system. The permeability has a stabilizing effect on stationary convection. Sharma and Kumar[4, 5] also studied the effect of magnetic field on the micropolar fluids heated from below in a non-porous and porous medium, they found that in the presence of various coupling parameters, the magnetic field has a stabilizing effect whereas the medium permeability has destabilizing effect on stationary convection. Reena and Rana[6] have studied the thermal convection of rotating micropolar fluid in hydromagnetic saturating a porous International Journal of Pure and Applied Mathematics Volume 118 No. 22 2018, 1393-1405 ISSN: 1314-3395 (on-line version) url: http://acadpubl.eu/hub Special Issue ijpam.eu 1393