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The effect of magnetic field dependent (MFD) viscosity on the onset of convection in a ferromagnetic fluid layer heated from below saturating rotating porous medium in the presence of vertical magnetic field is investigated theoretically by using Darcy model. The resulting eigen value problem is solved using the regular perturbation technique. Both stationary and oscillatory instabilities have been obtained. It is found that increase in MFD viscosity and increase in magnetic Rayleigh number is to delay the onset of ferroconvection, while the nonlinearity of fluid magnetization has no influence on the stability of the system.

The thermal perturbation method is employed for analytical solution. 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 impermeable boundaries for which an exact solution is obtained.

The conditions for the system to stabilize both by stationary and oscillatory modes are studied. Even for the oscillatory system of particular frequency dictated by physical conditions, the critical Rayleigh numbers for oscillatory mode of the system were found to be greater than for the stationary mode. The system gets destabilized for various physical parameters only through stationary mode. Hence, the analysis is restricted to the stationary mode. To the Coriolis force, the Taylor number T_a is calculated to discuss the results. It is found that the system stabilizes through stationary mode for values of and for oscillatory instability is favored for Ta > 104. Therefore the Taylor number T_a leads to stability of the system. For larger rotation, magnetization leads to destabilization of the system. The MFD viscosity is found to stabilize the system.

This research paper is new and original.

The purpose of the present paper is to investigate the thermo-mechanical interactions in an initially stressed nonlocal micropolar thermoelastic half-space having void pores under Lord–Shulman model. A moving thermal shock is applied to the formulation.

The normal mode technique is adopted to obtain the exact expressions of the physical quantities.

Numerical computations for stresses, displacement components, temperature field and change in the volume fraction field are performed for suitable material and are depicted graphically. Some comparisons have been shown in figures to estimate the effects of micropolarity, initial stress, voids, nonlocal parameter and time on the resulting quantities.

The exact expressions for the displacement components, stresses, temperature and change in the volume fraction field are obtained in the physical domain. Although numerous investigations do exist to observe the disturbances in a homogeneous, isotropic, initially stressed, micropolar thermoelastic half-space, the work in its current form has not been established by any scholar till now. The originality of the present work lies in the formulation of a fresh research problem to investigate the dependence of different physical fields on nonlocality parameters, micropolarity, initial stress, porosity and time due to the application of a moving thermal shock.

The purpose of this paper is to study two-dimensional deformations in a nonlocal, homogeneous, isotropic, rotating thermoelastic medium with temperature-dependent properties under the purview of the Green-Naghdi model II of generalized thermoelasticity. The formulation is subjected to a mechanical load.

The normal mode analysis technique is adopted to procure the exact solution of the problem.

For isothermal and insulated boundaries, discussions have been made to highlight the influences of rotational speed, nonlocality, temperature-dependent properties and time on the physical quantities.

The exact expressions for the displacement components, stresses and temperature field are obtained in the physical domain. These are also calculated numerically for a magnesium crystal-like material and depicted through graphs to observe the variations of the considered physical quantities. The present study is useful and valuable for the analysis of problems involving mechanical shock, rotational speed, nonlocal parameter, temperature-dependent properties and elastic deformation.

The purpose of this paper is to analyse the transient effects in a functionally graded photo-thermoelastic (TE) medium with gravity and rotation by considering two generalised TE theories: Lord–Shulman (LS) and Green–Lindsay (GL). The governing equations are derived in rectangular Cartesian coordinates for a two dimensional problem.

All the physical properties of the semiconductor are supposed to vary exponentially with distance. The analytical solution is procured by employing normal mode technique on the resulting non-dimensional coupled field equations with appropriate boundary conditions.

For the mechanically loaded thermally insulated surface, normal displacement, stress components, temperature distribution and carrier density are calculated numerically with the help of MATLAB software for a silicon semiconductor and displayed graphically. Some particular cases of interest have also been deduced from the present results.

The effects of rotation and non-homogeneity on the different physical fields are investigated on the basis of analytical and numerical results. Comparisons are made with the results predicted by GL theory in the presence and absence of gravity for different values of time. Comparisons are also made between the three theories in the presence of rotation, gravity and in-homogeneity. Such problems are very important in many dynamical systems.

The purpose of this study is to analyze the two-dimensional disturbances in a nonlocal, functionally graded, isotropic thermoelastic medium under the purview of the Green–Lindsay model of generalized thermoelasticity. The formulation is subjected to a mechanical load. All the thermomechanical properties of the solid are assumed to vary exponentially with the position.

Normal mode technique is proposed to obtain the exact expressions for the displacement components, stresses and temperature field.

Numerical computations have been carried out with the help of MATLAB software and the results are illustrated graphically. These are also calculated numerically for a magnesium crystal-like material and illustrated through graphs. Theoretical and numerical results demonstrate that the nonlocality and nonhomogeneity parameters have significant effects on the considered physical fields.

Influences of nonlocality and nonhomogeneity on the physical quantities are carefully analyzed for isothermal and insulated boundaries. The present work is useful and valuable for analysis of problems involving mechanical shock, nonlocal parameter, functionally graded materials and elastic deformation.

The purpose of this study is to analyze the disturbances in a two-dimensional nonlocal, micropolar elastic medium under the dual-phase-lag model of thermoelasticity whose surface is subjected to an inclined mechanical load. The present study is carried out under the influence of gravity.

The normal mode technique is used to obtain the exact expressions of the physical fields.

For inclined mechanical load, the impact of micropolarity, nonlocal parameter, gravity and inclination angle have been highlighted on the considered physical fields.

The numerical results are computed for various physical quantities such as displacement, stresses and temperature for a magnesium crystal-like material and are illustrated graphically. The study is valuable for the analysis of thermoelastic problems involving gravitational field, nonlocal parameter, micropolarity and elastic deformations.

The purpose of this paper is to establish a model of two-dimensional half-space problem of linear, isotropic, homogeneous, initially stressed, rotating thermoelastic medium with microtemperatures. The expressions for different physical variables such as displacement distribution, stress distribution, temperature field and microtemperatures are obtained in the physical domain.

Normal mode analysis technique is adopted to procure the exact solution of the problem.

Numerical computations have been carried out with the help of MATLAB programming, and the results are illustrated graphically. Comparisons are made to show the effects of rotation, time and microtemperatures on the resulting quantities. The graphical results indicate that the effects of rotation, microtemperatures and time are very pronounced on the field variables.

In the present work, we have investigated the effects of rotation, time and microtemperature in an initially stressed thermoelastic medium. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form, i.e. the disturbances in a thermoelastic medium in the presence of angular velocity, initial stress and microtemperature have not been studied till now. The present work is useful and valuable for analysis of problems involving coupled thermal shock, rotation parameter, microtemperatures and elastic deformation.

The present investigation is concerned with the two-dimensional deformations in an inhomogeneous fiber-reinforced thermoelastic medium under the influence of gravity in the context of Green–Lindsay theory.

Material properties are supposed to be graded in x-direction, and normal mode technique is adopted to obtain the exact expressions for the temperature field, displacement components and stresses.

Numerical computations have been carried out with the help of MATLAB software, and the results are depicted graphically to observe the disturbances induced in the considered medium. Comparisons made within the theory of the physical quantities are shown in figures to highlight the effects of fiber reinforcement, inhomogeneity parameter, gravity and time.

In the present work, we have investigated the effects of fiber reinforcement, inhomogeneity parameter, gravity and time in an inhomogeneous, fiber-reinforced thermoelastic medium under the influence of gravity. Although various investigations do exist to observe the disturbances in a thermoelastic medium under the effects of different parameters, the work in its present form i.e. thermally induced vibrations in an inhomogeneous fiber-reinforced thermoelastic material with gravity has not been studied till now. The present work is useful and valuable for analysis of problems involving thermal shock, gravity parameter, fiber reinforcement, inhomogeneous and elastic deformation.

The purpose of this paper is to study the transient thermoelastic interactions in a nonlocal rotating magneto-thermoelastic medium with temperature-dependent properties. Three-phase-lag (TPL) model of generalized thermoelasticity is employed to study the problem. An initial magnetic field with constant intensity acts parallel to the bounding plane. Therefore, Maxwell's theory of electrodynamics has been effectively introduced and the expression for Lorentz's force is obtained with the help of modified Ohm's law.

The normal mode technique has been adopted to solve the resulting non-dimensional coupled field equations to obtain the expressions of physical field variables.

For uniformly distributed thermal load, normal displacement, temperature distribution and stress components are calculated numerically with the help of MATLAB software for a copper material and the results are illustrated graphically. Some particular cases of interest are also deduced from the present study.

Influences of nonlocal parameter, rotation, temperature-dependent properties, magnetic field and time are carefully analyzed for mechanically stress free boundary and uniformly distributed thermal load. The present work is useful and valuable for analysis of problem involving thermal shock, nonlocal parameter, temperature-dependent elastic and thermal moduli.

This study aims to focus on the effect of hall currents on the thermal stability of a couple-stress fluid with a uniform horizontal magnetic field.

The thermal perturbation method is used for the analytical solution. The analysis is administered within the framework of linear stability theory and normal mode technique on the convection for a fluid layer contained between two boundaries for which an exact solution is obtained.

For the case of stationary convection, a dispersion relation governing the effect of hall currents magnetic field and couple stress are derived. Results from the current study concluded that magnetic field has stabilizing effect whereas hall currents are found to have a destabilizing effect on the system. Couple stress, however, has a dual character in contrast to its stabilizing effect in the absence of hall currents. The Oscillatory modes are introduced due to the presence of a magnetic field in the system. Graphs are plotted by giving numerical values to the parameters to depict the stability characteristics in each case.

This research paper is new and original.