Effect of Dust Particles on Rotating Micropolar Fluid Heated From Below Saturating a Porous Medium

This paper deals with the theoretical investigation of the effect of dust particles on a layer of rotating micropolar fluid heated from below saturating a 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. The principle of exchange of stabilities is found to hold true for the micropolar fluid saturating a porous medium heated from below in the absence of dust particles, rotation and micropolar heat conduction parameter. The oscillatory modes are introduced due to the presence of the dust particles and rotation, which were non-existence in their absence. The presence of micropolar heat conduction parameter may also introduce oscillatory modes. For the case of stationary convection, the effect of various parameters like medium permeability, rotation, dust particles, coupling parameter, micropolar coefficient (A) and micropolar heat conduction parameter has been analyzed. The thermal Rayleigh number for the onset of instability is also determined numerically and results are depicted graphically. In the present paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability

Nonlinear microstrain theories.

Abstract A hierarchy of higher order continua is presented that introduces additional degrees of freedom accounting for volume changes, rotation and straining of an underlying microstructure. An increase in the number of degrees of freedom represents a refinement of the material description. In addition to available nonlinear Cosserat and micromorphic theories, general formulations of elastoviscoplastic behaviour are proposed for microdilatation and microstretch continua. A microstrain theory is introduced that is based on six additional degrees of freedom describing the pure straining of the microstructural element. In each case, balance equations and boundary conditions are derived, decompositions of the finite strain measures into elastic and plastic parts are provided. The formulation of finite deformation elastoviscoplastic constitutive equations relies on the introduction of the free energy and dissipation potentials, thus complying with requirements of continuum thermodynamics. Some guidelines for the selection of a suitable higher order model for a given material close the discussion