Thermoconvective instability in multi-component FLUIDs has wide range of applications in heat and mass transfer. This paper deals with the theoretical investigation on a horizontal FLUID layer of MICROPOLAR FERROMAGNETIC FLUID heated from below and salted from above saturating a porous medium subjected to a transverse uniform magnetic field using Brinkman model. The salt is a FERROMAGNETIC salt which modifies the magnetic field established. The effect of salinity has been included in the magnetization and density of the FERROMAGNETIC FLUID. A theory of linear stability analysis and normal mode technique have been carried out to analyze the onset of convection for a FLUID layer contained between two free boundaries for which exact solution is obtained and the stationary and oscillatory instabilities have been carried out for various physical quantities. The results are depicted graphically and the stabilizing and destabilizing behaviors are studied.

Consideration is given to the problem of steady axisymmetric Stokes flow of a MICROPOLAR FLUID past a sphere coated with a thin, immiscible Newtonian FLUID layer. Inertial effects are neglected for both the outer FLUID and the FLUID film. The stream function solutions of the governing equations are obtained in terms of modified Bessel functions and Gegenbauer functions. The explicit expressions of flow fields are determined by applying the boundary conditions at the coated sphere interface and uniform velocity at infinity. The drag force experienced by the FLUID-coated sphere is evaluated and its variation is studied with respect to various geometric and material parameters. It is found that a sphere without coating experience greater resistance in comparison to coated FLUID. Some well-known results are then deduced from the present study.

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.

The combined effect of Hall current, Ohmic heating and suction/injection on the hydro-magnetic free convective heat transfer in a MICROPOLAR boundary layer flow past a vertical plate is analyzed. The FLUID is assumed to be viscous, incompressible and electrically conducting with a strong magnetic field. Using the modified Ohm’s law and the Bossinesq approximation the governing equations of the problem are transformed into a system of non-linear ordinary differential equations by introducing a suitable similarity transformation. The resulting boundary value problem is solved numerically by Nachtsheim-Swigert shooting technique with a sixth order Runge- Kutta iteration scheme. The results are obtained to study the effects of the governing parameters, suction/injection parameter (fW), magnetic parameter, Hall current parameter (m), material parameter (N1), microrotational parameter (G), the Prandtl number (Pr)and the Brinkman number (Br) on the transport behaviors of the FLUID. That is a parametric study is performed to illustrate the influence of these parameters on the velocity and temperature distribution as well as the local skin-friction and the local Nusselt number. Furthermore, the numerical solutions obtained in this study are compared with the existing results in the literature for some special values of Pr and the results are found to be in a good agreement.

The aim of this paper is to present numerically the transport mechanism of an incompressible MICROPOLAR FLUID between two vertical walls when the motion occurs due to the buoyancy force. The governing equations in non-dimensional form are solved numerically using the Matlab software. The obtained numerical solutions for the velocity and micro-rotation profiles are displayed using the graphs for various values of the vortex viscosity parameter and material parameter. It is found that the material parameter has retarding effect on the velocity of MICROPOLAR FLUID and to make the flow steady state earlier for both thermal conditions. The effect of the vortex viscosity parameter is to decrease the steady state time of the velocity and micro-rotation.

In this study, the heat transfer and the entropy generation is investigated for MICROPOLAR FLUID flow through an inclined channel of parallel plates with constant pressure gradient. The lower plate is maintained at constant temperature and upper plate at a constant heat flux. The governing equations which are continuity, momentum and energy are solved numerically by Wolfram Mathematica 11 software. The velocity, microrotation and temperature profiles are used to evaluate the entropy generation number. The effect of characteristic parameters is discussed on velocity, temperature, microrotation, entropy generation and Bejan number in different diagrams. The results reveal that the entropy generation number increases with the increase in Brinkman number. The nonlinear parameter affected the velocity, microrotation, temperature, entropy generation and Bejan number diagrams. The result shows that the entropy generation number increased with increasing the brinkman number. It reduced with increasing the values of nonlinear parameter, Prandtl number and Reynolds number. Also the effect of pressure gradient is investigated on velocity, temperature, microrotation, entropy generation and Bejan number in different diagrams.

In the present work a two FLUID model for blood flow through abnormally constricted human artery (stenosed artery) has been developed. The model consists of a core region of suspension of all erythrocytes assumed to be micro-polar FLUID so as to include the micro-structural effects in addition to the peripheral-layer viscosity effects, and a peripheral plasma layer free from cells of any kind of Newtonian FLUID. This model is used to predict the effects on physiological characteristics of blood flow in normal and stenosed condition. The significance of the present model over the existing models has been pointed out by comparing the results with other theories both analytically and numerically.

In this paper, squeeze film damping in a micro-beam resonator based on micro-polar FLUID theory has been investigated. The proposed model for this study consists of a clamped-clamped microbeam suspended between two fixed stratums. The gap between the micro-beam and stratums is filled with air. Equation of motion governing the transverse deflection of the micro-beam based on strain gradient theory and also non-linear Reynolds equation of the FLUID field based on MICROPOLAR theory have been non-dimensionalized, linearized and solved simultaneously to calculate the quality factor of the squeeze film damping. The effect of non-dimensional length scale parameter of the air and micro-beam for different values of micro-polar coupling parameter has been investigated. It has been shown that applying micro-polar theory underestimates and also applying strain gradient theory overestimates the values of quality factor that are obtained in the case of classic theory. The quality factor of the squeeze film damping for different values of nondimensional length of the beam, squeeze number and non-dimensional pressure have been calculated and compared to the obtained values of quality factor based on classic theory.