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In this study, the effect of Hall current on the criterion for the onset of MHD convection in a porous medium layer saturated by a nanofluid is investigated. The model used for nanofluid combines the effect of Brownian motion and thermophoresis, while for a porous medium Brinkman model is used. A physically more realistic boundary condition than the previous ones on the nanoparticle volume fraction is considered i.e. the nanoparticle flux is assumed to be zero rather than prescribing the nanoparticle volume fraction on the boundaries. Using linear stability theory, the exact analytical expression for critical Rayleigh Darcy number is obtained in terms of various non-dimensional parameters. Results indicate that the magnetic field, Hall current, porous medium and nanoparticles significantly influence the stability characteristics of the system. The increase in the Hall current parameter, the Lewis number, the modified diffusivity ratio and the concentration Rayleigh Darcy number is to hasten the onset of convection while the magnetic Darcy number, the porosity parameter and the Darcy number has stabilized on the onset of convection.

The present paper is devoted to the investigation of the influence of the rotation, thermal field, magnetic field and voids on the reflection of a P wave with one relaxation time. The basic governing equations for isotropic and homogeneous generalized thermoelastic half-spaces with voids, rotation and Maxwell’s stress are formulated in the context of the Lord Shulman theory. The boundary conditions at the stress-free thermally insulated surface are satisfied to obtain an algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves: P1, P 2, P3 and P4. In addition, the reflection coefficients from insulated and stress-free surfaces for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, magnetic field, thermal relaxation time and void parameters.

An analysis is presented to study the MHD free convection with thermal radiation and mass transfer of polar fluid through a porous medium occupying a semi-infinite region of the space bounded by an infinite vertical porous plate with constant suction velocity in the presence of chemical reaction, internal heat source, viscous and Darcy's dissipation. The highly nonlinear coupled differential equations governing the boundary layer flow, heat, and mass transfer are solved by using a two-term perturbation method with Eckert number as a perturbation parameter. The results are obtained for velocity, angular velocity, temperature, concentration, skin friction, Nusselt number, and Sherwood number. The effect of various material parameters on flow, heat, and mass transfer variables is discussed and illustrated graphically.

This paper analytically studies the thermal radiation and chemical reaction effect on unsteady MHD convection through a porous medium bounded by an infinite vertical plate. The fluid considered here is a gray, absorbing-emitting but nonscattering medium, and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The dimensionless governing equations are solved using Laplace transform technique. The resulting velocity, temperature and concentration profiles as well as the skin-friction, rate of heat, and mass transfer are shown graphically for different values of physical parameters involved.

Using a generalized thermoelastic solid half-space, we estimate the impact of magnetic field, initial pressure and hydrostatic initial stress on reflection of P and SV waves. We consider a Green Lindsay model and present the governing equations for an isotropic homogeneous generalized thermoelastic solid under a magnetic field and hydrostatic initial stress. Lame's potentials are used in two dimensions that tend to separate the governing equations into three equations that are sought in harmonic travelling wave form. We introduce the equations of the velocity of the P wave, thermal wave and SV wave. The boundary conditions for mechanical and Maxwell's stresses and thermal insulation are applied to determine the reflection coefficients for the P wave, thermal wave and SV wave. Some new aspects are obtained of the reflection coefficients and displayed graphically and new conclusions are presented. Finally, it is shown that, under some conditions, previous results are special cases of our results.Keywords: P wave1 SV wave1 Generalized thermoelasticity1 Magnetic field1 Reflection coefficients1 Hydrostatic and pressure stresses.

The present paper is devoted to investigate the influence of the rotation, thermal field, initial stress, gravity field, electromagnetic and voids on the reflection of P wave under three models of generalized thermoelasticity: Classical and Dynamical coupled model (CD), Lord-Shulman model (LS), Green-Lindsay model (GL), The boundary conditions at stress-free thermally insulated surface are satisfied to obtain Algebraic system of four equations in the reflection coefficients of various reflected waves. It is shown that there exist four plane waves; P1, P2, P3 and P4. In addition, the reflection coefficients from insulated and isothermal stress-free surface for the incident P wave are obtained. Finally, numerical values of the complex modulus of the reflection coefficients are visualized graphically to display the effects of the rotation, initial stress, gravity field magnetic field, thermal relaxation times and voids parameters.