Abstract:
The effects of result from the substitution of the classical Fourier law by the non-classical Maxwell-Cattaneo law on the Rayleigh-Bénard Magneto-convection in an electrically conducting micropolar fluid is studied using the Galerkin technique. The eigenvalue is obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations with isothermal or adiabatic temperature on the spin-vanishing boundaries. The influences of various micropolar fluid parameters are analyzed on the onset of convection. The classical approach predicts an infinite speed for the propagation of heat. The present non-classical theory involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigenvalues are less than the classical ones.

Abstract:
We apply Maxwell and Cattaneo's relaxation approaches to the analysis of strong shockwaves in a two-dimensional viscous heat-conducting fluid. Good agreement results for reasonable values of Maxwell's relaxation times. Instability results if the viscous relaxation time is too large. These relaxation terms have negligible effects on slower-paced subsonic problems, as is shown here for two-roll and four-roll Rayleigh-Benard flows.

Abstract:
The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Bénard convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations and for isothermal and/or adiabatic temperature boundaries. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters and electric Rayleigh number on the onset of convection has been analyzed. One linear and five non-uniform temperature profiles are considered and their comparative influence on onset is discussed.

The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Bénard-Marangoni convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for an upper free/adiabatic and lower rigid/isothermal boundaries. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters and electric Rayleigh number on the onset of convection has been analysed. Six different non-uniform temperature profiles are considered and their comparative influence on onset is discussed.

Abstract:
we establish the existence and uniqueness of the solution for the magneto-micropolar fluid equations in the case of exterior domains in ir 3 . first, we prove the existence of at least one weak solution of the stationary system. then we discuss its uniqueness.

Abstract:
By using the spectral Galerkin method, we prove a result on global existence in time of strong solutions for the motion of magneto-micropolar fluid without assuming that the external forces decay with time. We also derive uniform in time estimates of the solution that are useful for obtaining error bounds for the approximate solutions.

Abstract:
We establish the existence and uniqueness of the solution for the magneto-micropolar fluid equations in the case of exterior domains in IR 3 . First, we prove the existence of at least one weak solution of the stationary system. Then we discuss its uniqueness.

Abstract:
Extended theories are widely used in the literature to describe the relativistic fluid. The motivation for this is mostly due to the causality issues allegedly present in the first order theories. However, the decay of fluctuations in the system is also at stake when first order theories \emph{that couple heat with acceleration} are used. In this paper it is shown how the generic instabilities in relativistic fluids are not present when a Maxwell-Cattaneo type law is introduced in the system of hydrodynamic equations. Emphasis is made on the fact that the stabilization is only due to the difference in characteristic times for heat flux relaxation and instabilities onset. This gives further evidence that Eckart's like constitutive equations are responsible for the first order sytem exhibiting unphysical behavior.

Abstract:
In the present paper, the governing equations of a linear transversely isotropic micropolar piezoelectric medium are specialized for x-z plane after using symmetry relations in constitutive coefficients. These equations are solved for the general surface wave solutions in the medium. Following radiation conditions in the half-space, the particular solutions are obtained, which satisfy the appropriate boundary conditions at the stress-free surface of the half-space. A secular equation for Rayleigh type surface wave is obtained. An iteration method is applied to compute the non-dimensional wave speed of the Rayleigh surface wave for specific material parameters. The effects of piezoelectricity, non-dimensional frequency and non-dimensional material constant, charge free surface and electrically shorted surface are shown graphically on the wave speed of Rayleigh wave.

Abstract:
A problem on Rayleigh wave in a rotating half-space of an orthotropic micropolar material is considered. The governing equations are solved for surface wave solutions in the half space of the material. These solutions satisfy the boundary conditions at free surface of the half-space to obtain the frequency equation of the Rayleigh wave. For numerical purpose, the frequency equation is approximated. The nondimensional speed of Rayleigh wave is computed and shown graphically versus nondimensional frequency and rotation-frequency ratio for both orthotropic micropolar elastic and isotropic micropolar elastic cases. The numerical results show the effects of rotation, orthotropy, and nondimensional frequency on the nondimensional speed of the Rayleigh wave. 1. Introduction Material response to external stimuli depends heavily on the motions of its inner structures. Classical elasticity does not include this effect, where only translation degrees of freedom of material point of body are considered. Eringen [1] developed the linear micropolar theory of elasticity, which included the intrinsic rotations of the microstructure. It provides a model which can support body and surface couples and display high frequency optical branch of the wave spectrum. For engineering applications, it can model composites with rigid chopped fibres, elastic solid with rigid granular inclusions, and other industrial materials such as liquid crystals. The assumptions of isotropy in a solid medium may not capture some of significant features of the continuum responses of soils, geological materials, and composites. Iesan [2–4] studied some static problems in orthotropic micropolar elasticity. Kumar and Choudhary [5, 6] studied the mechanical sources and dynamic behaviour of orthotropic micropolar elastic medium. Kumar and Chaudhary [7] studied the plane strain problem in a homogeneous orthotropic micropolar elastic solid. Kumar and Ailawalia [8] studied the response of a micropolar cubic crystal due to various sources. Kumar and Gupta [9] studied the propagation of waves in transversely isotropic micropolar generalized thermoelastic half-space. Singh [10] investigated the two-dimensional plane wave propagation in an orthotropic micropolar elastic solid. Surface waves in elastic solids were first studied by Rayleigh [11] for an isotropic elastic solid. The extension of surface wave analysis and other wave propagation problems to anisotropic elastic materials has been the subject of many studies; see, for example, [12–21]. The aim of the present paper is to study the propagation of