Showing papers on "Hartmann number published in 2010"

Entropy analysis for viscoelastic magnetohydrodynamic flow over a stretching surface

Abstract: This paper presents the application of the second law analysis of thermodynamics to viscoelastic magnetohydrodynamic flow over a stretching surface. The velocity and temperature profiles are obtained analytically using the Kummer's functions and used to compute the entropy generation number. The effects of the magnetic parameter, the Prandtl number, the heat source/heat sink parameter and the surface temperature parameter on velocity and temperature profiles are presented. The influences of the same parameters, the Hartmann number, the dimensionless group parameter and the Reynolds number on the entropy generation are also discussed.

Hydromagnetic free convection flow with induced magnetic field effects

Abstract: An exact solution is presented for the hydromagnetic natural convection boundary layer flow past an infinite vertical flat plate under the influence of a transverse magnetic field with magnetic induction effects included. The transformed ordinary differential equations are solved exactly, under physically appropriate boundary conditions. Closed-form expressions are obtained for the non-dimensional velocity (u), non-dimensional induced magnetic field component (B x ) and wall frictional shearing stress i.e. skin friction function (τ x ) as functions of dimensionless transverse coordinate (η), Grashof free convection number (G r ) and the Hartmann number (M). The bulk temperature in the boundary layer (Θ) is also evaluated and shown to be purely a function of M. The Rayleigh flow distribution (R) is derived and found to be a function of both Hartmann number (M) and the buoyant diffusivity parameter (ϑ *). The influence of Grashof number on velocity, induced magnetic field and wall shear stress profiles is computed. The response of Rayleigh flow distribution to Grashof numbers ranging from 2 to 200 is also discussed as is the influence of Hartmann number on the bulk temperature. Rayleigh flow is demonstrated to become stable with respect to the width of the boundary layer region and intensifies with greater magnetic field i.e. larger Hartman number M, for constant buoyant diffusivity parameter ϑ *. The induced magnetic field (B x ), is elevated in the vicinity of the plate surface with a rise in free convection (buoyancy) parameter G r , but is reduced over the central zone of the boundary layer regime. Applications of the study include laminar magneto-aerodynamics, materials processing and MHD propulsion thermo-fluid dynamics.

Variable Viscosity on Magnetohydrodynamic Fluid Flow and Heat Transfer over an Unsteady Stretching Surface with Hall Effect

Abstract: The problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible, and electrically conducting fluid past a semi-infinite unsteady stretching sheet is analyzed numerically. The problem was studied under the effects of Hall currents, variable viscosity, and variable thermal diffusivity. Using a similarity transformation, the governing fundamental equations are approximated by a system of nonlinear ordinary differential equations. The resultant system of ordinary differential equations is then solved numerically by the successive linearization method together with the Chebyshev pseudospectral method. Details of the velocity and temperature fields as well as the local skin friction and the local Nusselt number for various values of the parameters of the problem are presented. It is noted that the axial velocity decreases with increasing the values of the unsteadiness parameter, variable viscosity parameter, or the Hartmann number, while the transverse velocity increases as the Hartmann number increases. Due to increases in thermal diffusivity parameter, temperature is found to increase.

Tayler instability of toroidal magnetic fields in MHD Taylor‐Couette flows

Abstract: The nonaxisymmetric Tayler instability (TI) of toroidal magnetic fields due to axial electric currents is studied for conducting incompressible fluids between two infinitely long corotating cylinders. For given Reynolds number of rotation the magnetic Prandtl number Pm of the liquid conductor and the ratio of the cylinder's rotation rates are the free parameters. It is shown that for resting cylinders the critical Hartmann number for instability does not depend on Pm hence the TI also exists in the limit Pm 0. By rigid rotation the instability is suppressed where for Pm = 1 the rotational quenching takes its maximum. Rotation laws with negative shear (i.e. dΩ /dR < 0) strongly destabilize the toroidal field if the rotation is not too fast. In galaxies with their quadrupolar magnetic field geometry this effect could have drastic implications. For sufficiently high Reynolds numbers of rotation, however, the TI completely disappears. For the considered magnetic constellation the superrotation laws support the rotational stabilization. The angular momentum transport of the instability is anticorrelated with the shear so that an eddy viscosity can be defined which proves to be positive. We have also shown the possibility of laboratory TI experiments with a wide-gap container filled with fluid metals like sodium or gallium. Even the effect of the rotational stabilization can be reproduced in the laboratory with electric currents of only a few kA (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

Abstract: An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented. A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy. The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity. The governing equations are solved by the perturbation technique and a numerical method. The analytical expressions for the velocity field, the temperature field, the induced magnetic field, the skin-friction, and the rate of heat transfer at the plate are obtained. The numerical results are demonstrated graphically for various values of the parameters involved in the problem. The effects of the Hartmann number, the chemical reaction parameter, the magnetic Prandtl number, and the other parameters involved in the velocity field, the temperature field, the concentration field, and the induced magnetic field from the plate to the fluid are discussed. An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values. The induced magnetic field along the x-direction increases with the increase in the Hartmann number, the magnetic Prandtl number, the heat source/sink, and the viscous dissipation. It is found that the flow velocity, the fluid temperature, and the induced magnetic field decrease with the increase in the destructive chemical reaction. Applications of the study arise in the thermal plasma reactor modelling, the electromagnetic induction, the magnetohydrodynamic transport phenomena in chromatographic systems, and the magnetic field control of materials processing.

MHD mixed convection flow in a vertical lid-driven square enclosure including a heat conducting horizontal circular cylinder with Joule heating

Abstract: In the present numerical investigation we studied the effect of magnetohydrodynamic (MHD) mixed convection flow in a vertical lid-driven square enclosure including a heat conducting horizontal circular cylinder with Joule heating. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin’s finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter (Hartmann number) Ha, Joule heating parameter J, Reynolds number Re and Richardson number Ri. The streamlines, isotherms, average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicated that the Hartmann number, Reynolds number and Richardson number have strong influence on the streamlines and isotherms. On the other hand, Joule heating parameter has little effect on the streamline and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.

Fully developed mhd flow of a micropolar and viscous fluids in a vertical porous space using ham

Abstract: The problem of MHD flow of two immiscible fluids through a vertical porous space in the presence of temperature dependent heat source is studied analytically with one region filled with micropolar fluid and the other region with a viscous fluid. The coupled non-linear equations governing the motion and energy are solved analytically using homotopy analysis method (HAM). These results are presented for various values of Hartmann number, permeability parameter, Grashof number, ratio of fluid heights, ratio of thermal conductivities, heat source parameter, micropolar fluid material parameter and Brinkmann number. The skin friction and the rate of heat transfer coefficient are obtained and discussed graphically.

Influence of magnetic field on the peristaltic flow of a viscous fluid through a finite-length cylindrical tube

Abstract: The paper presents an analytical investigation of the peristaltic transport of a viscous fluid under the influence of a magnetic field through a tube of finite length in a dimensionless form. The expressions of pressure gradient, volume flow rate, average volume flow rate and local wall shear stress have been obtained. The effects of the transverse magnetic field and electrical conductivity i.e. the Hartmann number on the mechanical efficiency of a peristaltic pump have also been studied. The reflux phenomenon is also investigated. It is concluded, on the basis of the pressure distribution along the tubular length and pumping efficiency, that if the transverse magnetic field and the electric conductivity increase, the pumping machinery exerts more pressure for pushing the fluid forward. There is a linear relation between the averaged flow rate and the pressure applied across one wavelength that can restrain the flow due to peristalsis. It is found that there is a particular value of the averaged flow rate corresponding to a particular pressure that does not depend on the Hartmann number. Naming these values 'critical values', it is concluded that the pressure required for checking the flow increases with the Hartmann number above the critical value and decreases with it below the critical value. It is also inferred that magneto-hydrodynamic parameters make the fluid more prone to flow reversal. The conclusion applied to oesophageal swallowing reveals that normal water is easier to swallow than saline water. The latter is more prone to flow reversal. A significant difference between the propagation of the integral and non-integral number of waves along the tube is that pressure peaks are identical in the former and different in the latter cases.

Unsteady MHD Couette Flows in an Annuli: The Riemann-Sum Approximation Approach

Abstract: The unsteady MHD Couette flow of a viscous incompressible electrically conducting fluid between two concentric horizontal cylinders of infinite length have been analysed when the outer cylinder has been set into uniform accelerated motion. A unified closed form expressions are derived corresponding to the cases of the magnetic field fixed relative to the fluid or to the accelerated outer cylinder. The well known Laplace transform technique is applied to solve the time-dependent governing equations, while the method of Riemann-sum approximation is employed to invert the Laplace domain to the time domain in order to obtain the velocity and the skin friction. The variations of the velocity and the skin friction with respect to the Hartmann number and time have been discussed.

Marginal turbulent magnetohydrodynamic flow in a square duct

Abstract: Direct numerical simulations using a high-order finite-difference method were performed of the turbulent flow in a straight square duct in a transverse magnetic field. Without magnetic field the turbulence can be maintained for values of the bulk Reynolds number above approximately Re=1077 [M. Uhlmann et al., “Marginally turbulent flow in a square duct,” J. Fluid Mech. 588, 153 (2007)]. In the magnetohydrodynamic case this minimal value of the bulk Reynolds number increases with the Hartmann number. The flow is laminar at Re=3000 when the Hartmann number is larger than Ha=12.5 and the flow is turbulent for Ha≦12.0. The secondary mean flow structure at Re=3000 consists of eight vortices located mainly at the Hartmann walls.

Effect of mass transfer on a flow in the magnetohydrodynamic squeeze film between two parallel disks with one porous disk

Abstract: An analysis has been performed on the magnetohydrodynamic squeeze flow between two parallel disks with the porosity of the disks taken into account. The disks, at time t*, are spaced a certain distance and a magnetic field is applied perpendicular to the disks. Approximate analytical solution via homotopy analysis method (HAM) is obtained, and the accuracy of this method has been verified by implemented numerical method. The effects of suction or injection, squeeze Reynolds number, and Hartmann number on the velocity profiles are studied.

Computation of a Rising Bubble in an Enclosure Filled with Liquid Metal under Vertical Magnetic Fields

Abstract: Three-dimensional numerical computations for a single bubble rising in a liquid metal within a rectangular enclosure in a uniform vertical magnetic field are carried out In this study, the bubble shape, the velocity field and the electric current density field interact with one another under the influence of the vertical magnetic field This is a triple simultaneous problem The pressure and the electric potential fields are obtained with an iterative procedure by the HSMAC method The numerical results exhibit that the rising velocity of the bubble for the range of Hartmann number 0 75 owing to deceleration effect on the fluid flow by the magnetic field The bubble elongates in the direction of the uniform magnetic field because of the modification of the pressure distribution by the Lorentz force

Mhd flow and heat transfer of two immiscible fluids between moving plates

Abstract: The magnetohydrodynamic (MHD) flow of two immiscible and electrically conducting fluids between isothermal, insulated moving plates in the presence of an applied electric and inclined magnetic field has been investigated in the paper. The partial differential equations governing the flow and heat transfer are solved analytically with appropriate boundary conditions for each fluid and these solutions have been matched at the interface. The numerical results for various values of the Hartmann number, the angle of magnetic field inclination, load parameter and the ratio of electrical and thermal conductivities have been presented graphically. It was found that decrease of magnetic field inclination angle flattens out the velocity and temperature profiles. With the increase of the Hartmann number velocity gradients near the plate’s increases, temperature in the middle of the channel decreases and near the plate’s increases. Induced magnetic field is evidently suppressed with an increase of the Hartman number. The effect of changes of the load factor is to aid or oppose the flow as compared to the short-circuited case.

Magnetohydrodynamic Natural Convection Flow in an Enclosure with a Finite Length Heater Using the Differential Quadrature (DQ) Method

Abstract: Analysis of heat and fluid flow transport due to natural convection and magnetohydrodynamic (MHD) flows in a square enclosure with a finite length heater has been performed using the differential quadrature (DQ) technique. The heater with constant heat flux is located on the bottom wall of the enclosure and isothermal boundary conditions are applied to the right vertical wall while the remaining walls are adiabatic. The effects of heater length (0.2 ≤ ϵ ≤ 0.8), heater location (0.1 ≤ c/L ≤ 0.9), and direction of magnetic force (0° ≤ φ ≤ 90°) for different values of Grashof (103 ≤ Gr ≤ 106) and Hartmann numbers (0 ≤ Ha ≤ 100) on the heat and fluid flow in the enclosure are studied. According to the results obtained, heat transfer reduces when increasing the Hartmann number. The rate of reduction is higher for high values of Grashof number. The heat transfer rate for the heater closer to the cold wall is considerably higher than the heaters far from the right wall.

MHD viscous flow and heat transfer induced by a permeable shrinking sheet with prescribed surface heat flux

Abstract: The problem of magnetohydrodynamic (MHD) boundary layer flow and heat transfer due to a permeable shrinking sheet with prescribed surface heat flux is studied. The viscous fluid is electrically conducting in the presence of a uniform applied magnetic field and the induced magnetic field is neglected. The transformed nonlinear ordinary differential equations are solved numerically via the implicit finite-difference scheme known as the Keller-box method. Both two-dimensional and axisymmetric cases are considered. The results for the skin friction coefficient and the wall temperature, as well as the velocity and temperature profiles are presented and discussed for various parameters. Dual solutions exist for certain range of the suction parameter and Hartmann number. It is found that the boundary layer separation is delayed with Hartmann number.

Mathematical modeling of oscillatory mhd couette flow in a rotating highly permeable medium permeated by an oblique magnetic field

Abstract: We study theoretically the incompressible, viscous, oscillatory hydromagnetic Couette flow in a horizontal fluid-saturated highly permeable porous medium parallel-plate channel rotating about an axis perpendicular to the plane of the plates under the action of a uniform magnetic field, B0, inclined at an angle θ to the axis of rotation. The flow is generated by the non-torsional oscillation of the lower plate of the channel. The reduced unsteady momentum equations are nondimensionalized with appropriate variables. Exact solutions under specified boundary conditions are obtained using the Laplace transform method (LTM). The flow regime is found to be controlled by a rotational parameter (K2), which is the reciprocal of the Ekman number (Ek), the square of the Hartmann magnetohydrodynamic number (M2), a porous medium permeability parameter (Kp), which is the inverse of the Darcy number (Da), oscillation frequency (ω), dimensionless time (T), and magnetic field inclination (θ). The influence of these paramet...

Perturbation solution to unsteady flow in a porous channel with expanding or contracting walls in the presence of a transverse magnetic field

Abstract: An incompressible flow in a porous channel with expanding or contacting walls in the presence of a transverse magnetic field is considered. Using similarity transformations, the governing equations are reduced to the nonlinear ordinary differential equations. The exact similar solutions for the different cases of the expansion ratio and the Hartmann number are obtained with a singular perturbation method, and the associated behavior is discussed in detail.

Analytical study of magnetohydrodynamic radiation-convection with surface temperature oscillation and secondary flow effects

Abstract: We study the steady and unsteady magnetohydrodynamic (MHD) viscous, incompressible free and forced convective flow of an electrically-conducting, Newtonian fluid in the presence of appreciable thermal radiation heat transfer and surface temperature oscillation. The fluid is assumed to be optically-thin and magnetic Reynolds number small enough to neglect induced hydromagnetic effects. Secondary (cross-flow) effects are incorporated. The governing equations are solved analytically using complex variables. Detailed computations of the influence of frequency of oscillation (), Hartmann number (M 2 ), radiation-conduction parameter (K1), Prandtl number (Pr), Grashof number (Gr) on the unsteady mean flow velocity (u1) and unsteady mean cross flow velocity (w1), the plate shear stresses for the unsteady main and the secondary flow and also temperature gradients due to the unsteady main flow and the unsteady cross flow, are presented graphically and tabulated. The closed-form solutions reveal that the shear stress component due to a steady mean flow experiences a non-periodic oscillation which varies as a function of the Hartmann number (M 2 ) and radiation parameter (K1). However the shear stress components due to main and cross flows for an unsteady mean flow are subjected to periodic oscillation which depend on Hartmann number, radiation parameter but also on the Prandtl number and frequency of oscillation. Applications of the model include fundamental magneto-fluid dynamics, MHD energy systems and magnetometallurgical processing for aircraft materials.

MHD convection with Soret and Dufour effects in a three-dimensional flow past an infinite vertical porous plate

Abstract: In this paper, the Soret and Dufour effects on a mixed convective mass transfer flow past an infinite vertical porous plate with transverse sinusoidal suction velocity in presence of a uniform transverse magnetic field have been studied analytically. The magnetic Reynolds number is assumed to be so small that the induced magnetic field can be neglected. The nondimensional equations governing the flow and heat and mass transfer are solved by regular perturbation technique, on the assumption that the solution consists of two parts: a mean part and a perturbed part. The expressions for the velocity, temperature and concentration fields, skin friction at the plate in the direction of the free stream, Nusselt number and Sherwood number at the plate, and the current density are obtained in nondimensional forms. The effects of the Hartmann number M, the Soret number Sr, the Dufour number Du, the Reynolds number Re, Schmidt number Sc, and the Prandtl number Pr on the flow and transport characteristics are discuss...

Magnetohydrodynamic poiseuille-couette flow and heat transfer in an inclined channel

Abstract: An analysis of the Poiseuille-Couette flow of two immiscible fluids between inclined parallel plates is investigated. One of the fluids is assumed to be electrically conducting while the other fluid and channel walls are assumed to be electrically insulating. The viscous and Ohmic dissipation terms are taken into account in the energy equation. The coupled nonlinear equations are solved both analytically valid for small values of the product of Prandtl number and Eckert number (= e) and numerically valid for all e. Solutions for large e reveal a marked change on the flow and rate of heat transfer. The effects of various parameters such as Hartmann number, Grashof number, angle of inclination, ratios of viscosities, widths and thermal conductivities are presented and discussed in detail.

Separation of species of a binary fluid mixture confined between two concentric rotating circular cylinders in presence of a strong radial magnetic field

Abstract: The effect of a radial magnetic field on separation of a binary mixture of incompressible viscous thermally and electrically conducting fluids confined between two concentric rotating circular cylinders with different angular velocity is examined. The equations governing the motion, temperature and concentration in cylindrical polar coordinate are solved analytically. The solution obtained in closed form for concentration distribution is plotted against the radial distances from the surface of the inner circular cylinder for various values of non-dimensional parameters. It is found that the non-dimensional parameters viz. the Hartmann number, thermal diffusion number, baro diffusion number, rotational Reynolds number, the product of Prandtl number and Eckert number, magnetic Prandtl number and the ratio of the angular velocities of inner and outer cylinders affects the species separation of rarer and lighter component significantly. The problem discussed here derives its application in the basic fluid dynamics separation processes to separate the rarer component of the different isotopes of heavier molecules where electromagnetic method of separation does not work.