%0 Journal Article
%T Double-Diffusive Magnetoconvection of a Dusty Micropolar Fluid Saturating a Porous Medium
%A Parul Aggarwal
%A Urvashi Gupta
%J ISRN Mathematical Physics
%D 2013
%R 10.1155/2013/789070
%X The paper deals with the theoretical investigation of the effect of dust/suspended particles on a layer of electrically conducting micropolar fluid heated and dissolved from below in the presence of a uniform vertical magnetic field in a porous medium. The presence of coupling between thermosolutal and micropolar effects and magnetic field brings oscillatory motions in the system. A dispersion relation governing the effects of solute gradient, magnetic field, and suspended particles is obtained for a fluid layer contained between two free boundaries using linear stability theory and normal mode technique. Graphs have been plotted by giving numerical values to various parameters involved to depict the stability characteristics for both cases of stationary convection and overstability. It has been found that, for permissible values of various parameters under consideration, the effect of magnetic field and solute gradient is stabilizing and that of medium permeability, suspended particles, and micropolar coefficient is destabilizing. Further it is found that the Rayleigh number for overstability is always less than that for stationary convection except for high values of suspended particle factor. 1. Introduction A general theory of micropolar fluids was originally introduced by Eringen [1¨C3] in order to describe some physical systems which do not satisfy the Navier-Stokes equations. These fluids differ from the classical fluids in the sense that they can support couple stresses due to rotatory motion. The equations governing the flow of a micropolar fluid involve a spin vector (microrotation vector) and a microinertia tensor (gyration parameter) in addition to the velocity vector. Thus the model of micropolar fluid will have six degrees of freedom of rigid body (three corresponding to translation and three corresponding to microrotation). Physically speaking, a micropolar fluid may be thought of as the fluid containing elongated molecules, for example, plasma, polymeric fluids, suspension solutions, liquid crystals, animal blood, paints, colloidal solutions, and muddy fluids like crude oils. Micropolar fluid stabilities have become an important field of research due to its significant importance in industry. Ahmadi [4] and P¨¦rez-Garc¨ªa and Rub¨ª [5] studied the effect of microstructures on thermal convection, and Lekkerkerker [6, 7], Bradley [8], and Laidlaw [9] investigated the existence of oscillatory motions. Chandrasekhar [10] presented the problem of thermal convection in a horizontal thin layer of Newtonian fluid heated from below under varying
%U http://www.hindawi.com/journals/isrn.mathematical.physics/2013/789070/