Thermal instability in a micropolar fluid layer subject to a magnetic field

In the present paper we have considered thermal instability in a heat conducting micropolar fluid layer under the influence of a transverse magnetic field. Assuming the bounding surfaces to be rigid the eigenvalue problem is solved using finite-difference and Wilkinson's iteration techniques. Here it is seen that the instability sets in not only for adverse temperature gradient but also for positive temperature gradient. Both the microtation and the magnetic field are seen to stabilize the fluid layer. However, the stabilizing effect of microrotation becomes less significant when the strength of the magnetic field is large. In the case of heating from below, the critical wave number is seen to be insensitive to increase in the strength of the magnetic field, while it increases significantly when the fluid is heated from above.     

Thermal instability in a nanofluid layer with a vertical magnetic field

The combined effect of a vertical magnetic field and the boundaries on the onset of convection in an electrically conducting nanofluid layer heated from below is investigated using linear stability theory. The employed model incorporates the effects of Brownian motion and thermophoresis. The boundaries are considered to be either rigid or free. The eigenvalue problem is solved analytically for free–free boundaries and numerically for rigid–rigid and lower-rigid and upper-free boundaries using the Galerkin technique. Numerical results are presented for alumina–water nanofluid.     

Dynamic and quasi-static behaviors of magneto-thermo-elastic stresses in a conducting infinite plate subjected to an arbitrary variation of magnetic field

Summary In the present paper, dynamic and quasi-static behaviors of magneto-thermo-elastic stresses in a conducting infinite plate subjected to an arbitrary variation of the magnetic field are investigated. It is assumed that a magnetic field defined by an arbitrary function of time acts on both side surfaces of the infinite plate in the direction parallel to its surfaces. Fundamental equations of one-dimensional electromagnetic, temperature and elastic fields are formulated. Then, solutions of magnetic field, eddy current, temperature change and both dynamic solutions and quasi-static ones of stresses and deformations in the infinite plate are derived analytically. The solutions of stresses are determined to be sums of thermal stress caused by eddy current loss and magnetic stress caused by Lorentz force. For the case that the arbitrary function is given by the sine function, the dynamic and quasi-static behaviors of the stresses are examined by numerical calculations.     

Thermal instability of rotating nanofluid layer

In the present paper we have considered thermal instability of rotating nanofluids heated from below. Linear stability analysis has been made to investigate analytically the effect of rotation. The more important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. Galerkin method is used to obtain the analytical expression for both non-oscillatory and oscillatory cases, when boundaries surfaces are free–free. The influence of various nanofluids parameters and rotation on the onset of convection has been analysed. It has been shown that the rotation has a stabilizing effect depending upon the values of various nanofluid parameters. The critical Rayleigh number for the onset of instability is determined numerically and results are depicted graphically. The necessary and sufficient conditions for the existence of over stability are also obtained.     

Impulsively started viscous flow past a finite flat plate with and without an applied magnetic field

Numerical methods are used to investigate the two-dimensional motion of a viscous incompressible fluid impulsively started past a flat plate of finite breadth at zero incidence to the uniform motion of the fluid at large distances from the plate. A step by step integration in time of Helmholtz's vorticity equation is used for Reynolds numbers 10–500. The magnetohydrodynamic case is also considered with the applied magnetic field at infinity parallel to the uniform stream and the non-conducting plate. Results for the Magnetic Reynolds number 50 and infinite, Viscous Reynolds number 50 and 0≤β≤2, where β is the ratio of the square of the Alfvén speed to the square of the main stream velocity, are presented.     

Dielectric behaviour of a ferrofluid subjected to a uniform magnetic field

The electric susceptibility of samples of ferrofluids subjected to a uniform magnetic fieldHwas measured. The electric susceptibilitychiis dependent on the magnitude of the magnetic field and on the relative direction between the electric fieldEand the magnetic fieldH. 1) WhenEis perpendicular toH, frac{partialchi_{perp}}{partialH} < 02) WhenEis parallel toH, frac{partialchi_{parellel}}{partialH} > 0These results have been interpreted as a magneto-electric directive effect. A model is proposed, based on the assumption that the magnetic particles are roughly ellipsoidal and conducting grains.     

Thermal stress state of a bimetallic plate subjected to pulsed electromagnetic action

We formulate a problem of thermomechanics for an infinite bimetallic plate of constant thickness subjected to nonstationary electromagnetic action and present a relationship for the evaluation of the load-carrying capacity of the plate. A procedure of approximate determination of the parameters of the electromagnetic fields, temperature, and stresses by using the quadratic approximation of the distribution of key functions over the thickness of layers of the plate is proposed. The solution of this problem is obtained for the electromagnetic action in the mode with pulsed modulating signal. We present the results of numerical investigation of the components of the stress tensor and stress intensities in the plane of contact of the constituent layers for a frequency of the carrier signal lying outside the neighborhood of the resonance frequencies and for the first resonance frequency. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 6, pp. 30–40, November–December, 2008.     

Streamlining of a cylinder with an electric arc rotating in a magnetic field

Streamlining of a circular cylinder with a localized heat source modeling an MHD actuator in which the plasma arc channel moves along the cylinder surface under the action of the Lorentz force in a radial magnetic field is studied experimentally and simulated numerically. It is shown that the presence of a moving heat release region leads to a break in the symmetry in cylinder streamlining by the external flow and the appearance of a nonzero lift force and circulation.     

A differential quadrature analysis of dynamic and quasi-static magneto-thermo-elastic stresses in a conducting rectangular plate subjected to an arbitrary variation of magnetic field

A rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical simulation of dynamic and quasi-static magneto-thermo-elastic stresses in a conducting rectangular plate subjected to an arbitrary variation of magnetic field. Fundamental equations of plane electromagnetic, temperature and elastic fields are formulated. To the best of the authors’ knowledge, this is the first attempt to apply the DQM to magneto-thermo-elasticity and the first attempt to analyze a finite two-dimensional magneto-thermo-elastic problem. The fundamental equations and the inhomogeneous time-dependent boundary conditions are discretized in spatial and temporal domain by differential quadrature (DQ) rules. The unknowns satisfying the governing equations, the boundary and initial conditions simultaneously are computed in the entire domain by means of DQM with high efficiency and accuracy using dramatically less grid points in both spatial and time domain. Solutions of magnetic field, eddy current, temperature change and dynamic solutions of stresses and deformations are illustrated graphically.     

Brownian relaxation of interacting magnetic nanoparticles in a colloid subjected to a pulsatile magnetic field

We have investigated and modeled the effect of interaction among magnetic particles and the magnitude and duration of external applied magnetic field on Brownian relaxation in a colloidal suspension. In the case of interacting magnetic particles, Brownian relaxation depends on the interparticle dipole-dipole interaction, which slows down the overall Brownian relaxation process of magnetic particles in the colloidal suspension. The individual magnetic particle experiences torque when a pulsatile magnetic field is applied. The torque due to the external field randomizes the particle rotation similar to that of the thermal energy. A faster Brownian relaxation is observed when individual magnetic particles are magnetized for a short duration. Magnetizing the magnetic particle for a longer duration suppress the rotational motion hence the effect of torque on Brownian relaxation.     

Propagation of waves in magneto-thermo-viscoelastic solids subjected to a uniform magnetic field

The propagation of magneto-thermo-mechanical (MTM) plane waves in electrically and thermally conductive magneto-thermo-viscoelastic (MTVE) unbounded solids is investigated with account for the mutual effects of the magnetic, thermal and strain fields. Concerning the mutual and thermo-electric effects in isotropic solids the governing equations are first linearized. In the linearization, the material is assumed to be subjected to a uniform and primary magnetic field in any direction while the material undergoes infinitesimal deformations. It is shown that the governing equations at the intermediate state are fulfilled by the presumed MTM-fields. Furthermore, the dispersion relation which allows us to consider the entire frequency range, the effect of the magnetic field and some nondimensional material parameters is obtained. Therefore, several modes of MTM-waves arise depending upon the direction of the magnetic field such as the uncoupled magnetic and mechanical S-mwaves, the coupled S-wave, the modified mechanical $\text{P}$-and thermal waves, and the modified and coupled MTM-waves. It is seen that all modes of the wave are dispersive and dissipative due to the conductivity and the viscosity of the material. Then the phase velocities and the attenuation constants for the coupling modes are obtained, and some limiting values are discussed. From the expressions follow, in particular, the results for the elastic case, the propagation of mechanical waves in nonconductive materials.     

Effect of spanwise rotation on centrifugal instability in rotating curved non-isothermal flows

 The effect of spanwise rotation on the centrifugal instability is examined numerically in terms of flow structure transitions by a finite volume method. The specific problem considered is a steady, hydrodynamically and thermally fully developed flow in a square duct with a strong streamwise curvature, a spanwise rotation in both positive and negative directions and wall cooling. The rotation is found to be of considerable effect on flow structures. As well the effect is more complex for non-isothermal flows due to a buoyancy force which increases with the square of the rotation speed. Several hitherto unknown flow structures are revealed. The results cover both transitions in flow structures and effects of the flow transitions on temperature distributions.     

Stochastic stability of a plate in a magnetic field

Summary The almost sure asymptotic and the uniform stochastic stability of a rectangular, beam-like, conducting plate in an exterior, normal to the plate middle surface magnetic field are investigated. The plate is simply supported on the two opposite edges and subjected to time-varying compressing forces which are assumed to be Gaussian stochastic processes. The problem is solved by means of the direct Liapunov functionals method. The uniform stability and the almost sure asymptotic stability regions are obtained for white and non-white compressing processes respectively. The influence of material magnetic properties on the stability regions is investigated.With 4 Figures     

Thermal boundary layers in magnetohydrodynamic flow over a flat plate in the presence of a transverse magnetic field

Summary A boundary layer solution for the heat transfer of an electrically conducting fluid over a semi-infinite flat plate in the presence of a transverse magnetic field has been studied. The heat due to viscous dissipation and stress work were also included into the energy equation. The governing nonsimilar partial differential equations are transformed into ordinary differential ones by means of difference-differential method. The temperature profiles and heat transfer coefficient are obtained for various values of the parameters entering the problem.     

MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation.     

Stability of ferrofluid flow between concentric rotating cylinders with an axial magnetic field

A linear stability analysis for the ferrofluid flow between two concentric rotating cylinders in the presence of an axial magnetic field is implemented in this study. Both of the wide-gap and small-gap cases are considered and the governing equations with respect to three-dimensional disturbances including axisymmetric and non-axisymmetric modes are derived and solved by a direct numerical procedure. A parametric study covering wide ranges of ?, the volume fraction of colloidal particles; ξ, the strength of axial magnetic field; μ, the ratio of angular velocity of the outer cylinder to that of the inner cylinder; and ε, the ratio of radius of the inner cylinder to that of the outer cylinder, is conducted. Results show that the stability characteristics depend heavily on these factors. It is found that the increases of ? and ξ, and decrease of ε tend to stabilize the basic flow for an assigned value of μ. The variations of the onset mode with these parameters are discussed in detail. An example for the practical application of present results is given to help the understanding of stability behaviour of this flow.