Heat transfer in MHD flow of dusty viscoelastic (Walters’ liquid model-B) stratified fluid in porous medium under variable viscosity

The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle θ. A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.     

Effect of the ion slip on the MHD flow of a dusty fluid with heat transfer under exponential decaying pressure gradient

In the present study, the unsteady Hartmann flow with heat transfer of a dusty viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied without neglecting the ion slip. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field applied perpendicular to the plates. The equations of motion are solved analytically to yield the velocity distributions for both the fluid and dust particles. The energy equations for both the fluid and dust particles including the viscous and Joule dissipation terms, are solved numerically using finite differences to get the temperature distributions.     

Influence of thermophoresis on heat and mass transfer under non-Darcy MHD mixed convection along a vertical flat plate embedded in a porous medium in the presence of radiation

The paper presents an investigation of the influence of thermophoresis on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid along a vertical flat plate with radiation effects. The plate is permeable and embedded in a porous medium. To describe the deviation from the Darcy model the Forchheimer flow model is used. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The nonlinear ordinary differential equations are linearized by using quasilinearization technique and then solved numerically by using implicit finite difference scheme. The numerical results are analyzed for the effects of various physical parameters such as magnetic parameter Ha, mixed convection parameter Ra _d /Pe _d , Reynolds number Red, radiation parameter R, thermophoretic parameter τ, Prandtl number Pr, and Schmidt number Sc. The heat transfer coefficient is also tabulated for different values of physical parameters.     

Effects of thermal radiation on the MHD flow past a vertical plate

The effects of thermal radiation on the MHD flow over a vertical and porous plate of an optically thin gray, electrically conducting, viscous and incompressible fluid are studied. The differential equations and their boundary conditions, describing the problemunder consideration, are dimensionalized and the numerical solution is obtained. The numerical results for the velocity and temperature profiles are shown for different dimensionless parameters entering the problem under consideration, such as the radiation parameter S, Grashof number G, Prandtl number P, and the magnetic parameter M.     

Stability of hydromagnetic Dean flow between two arbitrarily spaced concentric circular cylinders in the presence of a uniform axial magnetic field

The effect of a uniform axial magnetic field on the stability of the flow of an incompressible viscous electrically conducting fluid between two arbitrarily spaced concentric circular cylinders driven by a constant azimuthal pressure gradient is studied. The linearized stability equations for steady axisymmetric disturbances form an eigenvalue problem, which are solved by using a classical Runge–Kutta scheme combined with a shooting method, termed unit disturbance method. It is observed that for fixed gap width, the magnetic field has a stabilizing influence on the flow for both perfectly conducting and nonconducting walls. It is also found that for a given value of magnetic parameter, stabilization is more as the gap width increases. Further the electrically nonconducting walls are found to be more destabilizing than the perfectly conducting walls. The critical value of the radii ratio (0<η<1) beyond which the first unstable mode becomes nonaxisymmetric is determined for various values of the magnetic parameter.     

Steady hydromagnetic flow between two porous concentric circular cylinders

The problem considered here is to study the MHD effects on the steady flow of an incompressibe viscous conducting fluid through two concentric porous non-conducting infinite circular cylinders, rotating in various ways with uniform angular velocities in presence of a radial magnetic field. It is supposed that the rate of suction at the inner cylinder is equal to the rate of injection at the outer.     

Hall effect on Hartmann flow and heat transfer of a Burgers' fluid

The effect of Hall current on the steady magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers' fluid between two parallel electrically insulating infinite planes is studied. The MHD flow is generated by applying constant pressure gradient. An external uniform magnetic field normal to the disks is applied. The disks are kept at two different constant temperatures. Exact solutions are obtained for the governing momentum and energy equations. The effects of Hartmann number M, Reynolds number Re, Prandtl number Pr, Eckert number Ec, pressure gradient dp/dx and Hall parameter η are examined.     

MHD oscillatory flow on free convection–radiation through a porous medium with constant suction velocity

Unsteady two-dimensional hydromagnetic free convection and thermal radiation flow of an electrically conducting viscous-incompressible fluid, through a highly porous medium bounded by a vertical plane surface of constant temperature are presented. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. Expressions for the velocity and temperature are obtained. The free-stream velocity of the fluid vibrates about a mean constant value and the surface absorbs the fluid with constant velocity. Effects of varying R (radiative parameter), G (Grashof number), k′ (permeability of the porous medium) and M (magnetic parameter upon the velocity field and the effect of varying R and Pr (Prandtl number) on the temperature are discussed.     

Heat Transfer in an Upper Convected Maxwell Fluid with Fluid Particle Suspension

An analysis is carried out to study the magnetohydrodynamic (MHD) flow and heat transfer characteristics of an electrically conducting dusty non-Newtonian fluid, namely, the upper convected Maxwell (UCM) fluid over a stretching sheet. The stretching velocity and the temperature at the surface are assumed to vary linearly with the distance from the origin. Using a similarity transformation, the governing nonlinear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and the equations are solved numerically by a second order finite difference implicit method known as the Keller-box method. Comparisons with the available results in the literature are presented as a special case. The effects of the physical parameters on the fluid velocity, the velocity of the dust particle, the density of the dust particle, the fluid temperature, the dust-phase temperature, the skin friction, and the wall-temperature gradient are presented through tables and graphs. It is observed that, Maxwell fluid reduces the wall-shear stress. Also, the fluid particle interaction reduces the fluid temperature in the boundary layer. Furthermore, the results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the dusty UCM fluid flow phenomena.     

Effect of couple stresses on transient MHD poiseuille flow

The unsteady laminar flow of an electrically conducting viscous fluid between parallel insulating plates subject to a transverse magnetic field is considered. The plates are fixed and flow is due to a constant pressure gradient. The induced field is taken into account. The fluid is incompressible and of couple stress type. The defining equations are coupled and numerical solutions for different values of couple stress parameter are obtained. The velocity and induced magnetic field profiles are sketched as functions of time, Hartmann number, and magnetic Prandtl number. The velocity decreases with increase in couple stress parameter.     

Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

The Equations of Magnetohydrodynamics: On the Interaction Between Matter and Radiation in the Evolution of Gaseous Stars

We prove existence of global-in-time weak solutions to the equations of magnetohydrodynamics, specifically, the Navier-Stokes-Fourier system describing the evolution of a compressible, viscous, and heat conducting fluid coupled with the Maxwell equations governing the behaviour of the magnetic field. The result applies to any finite energy data posed on a bounded spatial domain in R ³, supplemented with conservative boundary conditions.The work supported by Grant A1019302 of GA AV CR     

Role of radial magnetic field on heat transfer in MHD Couette flow in an annulus with viscous and Joule dissipation

This paper presents an analytical investigation of steady, fully developed MHD Couette flow of viscous, incompressible, electrically conducting fluid in the presence of radial magnetic field. Exact solutions are derived for the governing energy and momentum equations by taking into account the effects of viscous and Joule dissipations under relevant boundary conditions. The solutions obtained are graphically represented and the effects of various controlling parameters such as Hartmann number and Brinkman number on the temperature profile and consequently the Nusselt numbers are discussed. The significant result from the study is that increase in Hartmann number leads to enhancement on the Nusselt number at outer surface of inner cylinder while the role of Hartmann number is just reverse on Nusselt number at inner surface of outer cylinder. In addition, the Brinkman number has an insignificant effect on the Nusselt numbers when both surfaces are kept at equal temperature.     

Fractional Green–Naghdi theory for thermoelectric MHD

ABSTRACT

In this work, we use the Green–Naghdi theory of thermomechanics of continua to derive a linear theory of MHD thermoelectric fluid with fractional order of heat transfer. This theory permits propagation of thermal waves at finite speed. The one-dimensional model of the theory is applied to Stokes’ flow of unsteady incompressible fluid due to a moving flat plate in the presence of both heat sources and a transverse magnetic field. The problem was solved using the Laplace transform technique. The solution in the transformed domain is obtained by a direct approach. A numerical method based on a Fourier-series expansion is used for the inversion process. The thermoelectric effects with fractional parameter on the temperature and velocity fields are analyzed and discussed in detail with the aid of graphical illustrations.     

Effects of hall current on MHD Couette flow in a rotating system with arbitrary magnetic field

Author has studied the MHD Couette flow in a rotating environment with non- conducting walls in the presence of an arbitrary magnetic field. The solution in dimensionless form contains four pertinent flow parameters, viz. the Hartmann number, the rotation parameter which is the reciprocal of the Ekman number, the Hall current parameter, and the angle of inclination of the magnetic field to the positive direction of the axis of rotation. An interplay of hydromagnetic force and Coriolis force with an inclusion of Hall current plays a significant role in determining the MHD flow behaviour. The velocity and induced magnetic field distributions are depicted graphically. Also, the numerical results of shear stresses and the rate of mass flows are presented graphically.     

Serrin-Type Blowup Criterion for Viscous, Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows

This paper establishes a blowup criterion for the three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic (MHD) flows. It is essentially shown that for the Cauchy problem and the initial-boundary-value one of the three-dimensional compressible MHD flows with initial density allowed to vanish, the strong or smooth solution exists globally if the density is bounded from above and the velocity satisfies Serrin’s condition. Therefore, if the Serrin norm of the velocity remains bounded, it is not possible for other kinds of singularities (such as vacuum states vanishing or vacuum appearing in the non-vacuum region or even milder singularities) to form before the density becomes unbounded. This criterion is analogous to the well-known Serrin’s blowup criterion for the three-dimensional incompressible Navier-Stokes equations, in particular, it is independent of the temperature and magnetic field and is just the same as that of the barotropic compressible Navier-Stokes equations. As a direct application, it is shown that the same result also holds for the strong or smooth solutions to the three-dimensional full compressible Navier-Stokes system describing the motion of a viscous, compressible, and heat conducting fluid.     

Rotational properties of annulus dusty plasma in a strong magnetic field

The collective dynamics of an annulus dusty plasma formed between a co-centric conducting (non-conducting) disk and ring configuration is studied in a strongly magnetized radiofrequency (rf) discharge. A superconducting electromagnet is used to introduce a homogeneous magnetic field to the dusty plasma medium. In the absence of the magnetic field, the dust grains exhibit thermal motion around their equilibrium position. The dust grains start to rotate in the anticlockwise direction with increasing magnetic field (B > 0.02 T ), and the constant value of the angular frequency at various strengths of the magnetic field confirms the rigid body rotation. The angular frequency of dust grains linearly increases up to a threshold magnetic field (B > 0.6 T ) and after that its value remains nearly constant in a certain range of magnetic field. Further increase in magnetic field (B > 1 T ) lowers the angular frequency. Low value of the angular frequency is expected by reducing the width of the annulus dusty plasma or the input rf power. The azimuthal ion drag force due to the magnetic field is assumed to be the energy source which drives the rotational motion. The resultant radial electric field in the presence of a magnetic field determines the direction of rotation. The variation of floating (plasma) potential across the annular region at given magnetic field explains the rotational properties of the annulus dusty plasma in the presence of a magnetic field.     

A note on unsteady hydromagnetic flow in a rotating channel permeated by an inclined magnetic field in the presence of an oscillator

Ghosh [Czech. J. Phys.46 (1996) 85] has extended the problem of an unsteady hydromagnetic flow (MHD) in a rotating environment permeated by an inclination of a uniform magnetic field with the positive direction of the axis of rotation; a fluid-pulse oscillator is applied along the axis of rotation in order to explain the validity of a physical situation of a steady flow under the conditions and configurations as stated by Ghosh in the paper cited above. It is investigated that the unsteady MHD flow has an intrinsic stability subject to Ghosh inertial frequency in relation withG _MK ² =(16K ⁴ −M ⁴ sin⁴ θ)^1/2, where MHD flow stability parameter of the Earth’s liquid core is taken into account, which seems to have disappeared in the literature since 1942. It is important to say that the thermonuclear reaction indicates a maximum dissipation of energy into smallest eddies when the kinetic energy is transformed into heat.     

Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator

In this paper we investigate the three-dimensional magnetohydrodynamic (MHD) rotating flow of a viscous fluid over a rotating sphere near the equator. The Navier-Stokes equations in spherical polar coordinates are reduced to a coupled system of nonlinear partial differential equations. Self-similar solutions are obtained for the steady state system, resulting from a coupled system of nonlinear ordinary differential equations. Analytical solutions are obtained and are used to study the effects of the magnetic field and the suction/injection parameter on the flow characteristics. The analytical solutions agree well with the numerical solutions of Chamkha et al. [31]. Moreover, the obtained analytical solutions for the steady state are used to obtain the unsteady state results. Furthermore, for various values of the temporal variable, we obtain analytical solutions for the flow field and present through figures.     

Effect of melting heat transfer and thermal radiation on Casson fluid flow in porous medium over moving surface with magnetohydrodynamics

In this study, the effects of variable fluid properties on heat transfer in MHD Casson fluid melts over a moving surface in a porous medium in the presence of the radiation are examined. The relevant similarity transformations are used to reduce the governing equations into a system of highly nonlinear ordinary differential equations and those are then solved numerically using the Runge–Kutta–Fehlbergmethod. The effects of different controlling parameters, namely, the Casson parameter,melting and radiation parameters, Prandtl number,magnetic field, porosity, viscosity and the thermal conductivity parameters on flow and heat transfer are investigated. The numerical results for the dimensionless velocity and temperature as well as friction factor and reducedNusselt number are presented graphically and discussed. It is found that the rate of heat transfer increases as the Casson parameter increases.