Showing papers on "Hartmann number published in 2013"

Heat transfer analysis for stretching flow over a curved surface with magnetic field

Abstract: The analysis of a viscous fluid flow and heat transfer is carried out under the influence of a constant applied magnetic field over a curved stretching sheet. Heat transfer analysis is carried out for two heating processes, namely, prescribed surface temperature (PST) and prescribed heat flux (PHF). The equations governing the flow are modeled in a curvilinear coordinate system (r, s, z). The nonlinear partial differential equations are then transformed to nonlinear ordinary differential equations by using similarity transformations. The obtained system of equations is solved numerically by a shooting method using Runge-Kutta algorithm. The interest lies in determining the influence of dimensionless radius of curvature on the velocity, temperature, skin friction, and rate of heat transfer at the wall prescribed by the Nusselt number. The effects of Hartmann number are also presented for the fluid properties of interest.

Numerical simulation of the Tayler instability in liquid metals

Abstract: The electrical current through an incompressible, viscous and resistive liquid conductor produces an azimuthal magnetic field that becomes unstable when the corresponding Hartmann number exceeds a critical value of the order of 20. This Tayler instability (TI), which is not only discussed as a key ingredient of a nonlinear stellar dynamo model (Tayler-Spruit dynamo), but also as a limiting factor for the maximum size of large liquid metal batteries, was recently observed experimentally in a column of a liquid metal (Seilmayer et al 2012 Phys. Rev. Lett. 108 244501). On the basis of an integro-differential equation approach, we have developed a fully three-dimensional numerical code, and have utilized it for the simulation of the Tayler instability at typical viscosities and resistivities of liquid metals. The resulting growth rates are in good agreement with the experimental data. We illustrate the capabilities of the code for the detailed simulation of liquid metal battery problems in realistic geometries.

Lattice Boltzmann simulation of natural convection in nanofluid-filled 2D long enclosures at presence of magnetic field

Abstract: In this paper, the effects of a magnetic field on natural convection flow in filled long enclosures with Cu/water nanofluid have been analyzed by lattice Boltzmann method. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 103–105, the volumetric fraction of nanoparticles between 0 and 6 %, the aspect ratio of the enclosure between A = 0.5 and 2. The Hartmann number has been varied from Ha = 0 to 90 with interval 30 while the magnetic field is considered at inclination angles of θ = 0°, 30°, 60° and 90°. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and the aspect ratios. Heat transfer decreases with the growth of the aspect ratio but this growth causes the effect of the nanoparticles to increase. The magnetic field augments the effect of the nanoparticles at high Rayleigh numbers (Ra = 105). The effect of the nanoparticles rises for high Hartmann numbers when the aspect ratio increases. The rise in the magnetic field inclination improves heat transfer at aspect ratio of A = 0.5.

Study of instabilities and quasi-two-dimensional turbulence in volumetrically heated magnetohydrodynamic flows in a vertical rectangular duct

Abstract: We consider magnetohydrodynamic (MHD) rectangular duct flows with volumetric heating. The flows are upward, subject to a strong transverse magnetic field perpendicular to the temperature gradient, such that the flow dynamics is quasi-two-dimensional. The internal volumetric heating imitates conditions of a blanket of a fusion power reactor, where a buoyancy-driven flow is imposed on the forced flow. Studies of this mixed-convection flow include analysis for the basic flow, linear stability analysis and Direct Numerical Simulation (DNS)-type computations. The parameter range covers the Hartmann number (Ha) up to 500, the Reynolds number (Re) from 1000 to 10 000, and the Grashof number (Gr) from 105 to 5 × 108. The linear stability analysis predicts two primary instability modes: (i) bulk instability associated with the inflection point in the velocity profile near the “hot” wall and (ii) side-wall boundary layer instability. A mixed instability mode is also possible. An equation for the critical Hartmann number has been obtained as a function of Re and Gr. Effects of Ha, Re, and Gr on turbulent flows are addressed via nonlinear computations that demonstrate two characteristic turbulence regimes. In the “weak” turbulence regime, the induced vortices are localized near the inflection point of the basic velocity profile, while the boundary layer at the wall parallel to the magnetic field is slightly disturbed. In the “strong” turbulence regime, the bulk vortices interact with the boundary layer causing its destabilization and formation of secondary vortices that may travel across the flow, even reaching the opposite wall. In this regime, the key phenomena are vortex-wall and various vortex-vortex interactions. Flow and magnetic field effects on heat transfer are also analyzed.

Effect of Induced Magnetic Field on Natural Convection in Vertical Concentric Annuli Heated/Cooled Asymmetrically

Abstract: In the present paper, the fully developed laminar free convective flow of a viscous incompressible and electrically conducting fluid between two concentric vertical cylinders is considered in the presence of a radial magnetic field. The induced magnetic field produced by the motion of an electrically conducting fluid is taken into account. The expressions for the temperature, velocity, induced magnetic field, induced current density, skin-friction and Nusselt number are obtained in a closed form under more general boundary conditions for the induced magnetic field. The influence of the Hartmann number and buoyancy force distribution parameter on the fluid velocity, induced magnetic field and induced current density have been analyzed by using the graphs while the values of the skin-friction, Nusselt number, induced current flux and mass flux are given in the tabular form. It is observed that the fluid velocity and induced magnetic field are rapidly decreasing with increase in the value of Hartmann number in the case when one of the cylinders is conducting compared with the case when both cylinders are non-conducting. The effect of the induced magnetic field is to increase the velocity profiles in comparison to the case of neglecting the induced magnetic field. The buoyancy force distribution parameter has tendency to increase the fluid velocity, induced magnetic field, temperature field and induced current flux.

Nanofluid Flow in a Semi-porous Channel in the Presence of Uniform Magnetic Field

Abstract: In this paper, the problem of laminar nanofluid flow in a semi-porous channel is investigated analytically using Homotopy Perturbation Method (HPM). This problem is in the presence of transverse magnetic field. Here, it has been attempted to show the capabilities and wide-range applications of the Homotopy Perturbation Method in comparison with the numerical method in solving such problems. The fluid is water containing copper as nanoparticle. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell–Garnetts (MG) and Brinkman models, respectively. The obtained solutions, in comparison with the out of the numeric methods admit a remarkable accuracy. A clear conclusion can be drawn from the numerical method’s (NM) results; the mentioned method provides high accurate solutions for nonlinear differential equations. Then, we consider the influence of the three dimensionless numbers: the nanofluid volume friction, Hartmann number for the description of the magnetic forces and the Reynolds number for the dynamic forces. Finally results and discussions are made at the end of this investigation.

Magnetohydrodynamics Thermocapillary Marangoni Convection Heat Transfer of Power-Law Fluids Driven by Temperature Gradient

Abstract: This paper presents an investigation for magnetohydrodynamics (MHD) thermocapillary Marangoni convection heat transfer of an electrically conducting power-law fluid driven by temperature gradient. The surface tension is assumed to vary linearly with temperature and the effects of power-law viscosity on temperature fields are taken into account by modified Fourier law for power-law fluids (proposed by Pop). The governing partial differential equations are converted into ordinary differential equations and numerical solutions are presented. The effects of the Hartmann number, the power-law index and the Marangoni number on the velocity and temperature fields are discussed and analyzed in detail.

Magnetohydrodynamic Natural Convection of Nanofluids in U-shaped Enclosures

Abstract: This article presents the results of a numerical study of laminar natural convection in a U-shaped enclosure that is filled with a water-Cu nanofluid and is under the influence of a horizontal magnetic field. A computational domain was defined and a numerical scheme based on the control volume formulation using the SIMPLE algorithm was developed. The convection-diffusion terms were discretized using a power-law scheme. The effects of the Rayleigh number, the solid volume fraction, the Hartmann number, and the enclosure aspect ratio on the heat transfer performance of the enclosure were examined. The thermal performance of the enclosure was found to be a function of the enclosure aspect ratio. The results also showed that the heat transfer rate increased with an increase of the Rayleigh number and the solid volume fraction, but it decreased with an increase of the Hartmann number.

Numerical Investigation of the Effect of Magnetic Field on Natural Convection in a Curved-Shape Enclosure

Abstract: This investigation reports the magnetic field effect on natural convection heat transfer in a curved-shape enclosure. The numerical investigation is carried out using the control volume-based-finite element method (CVFEM). The numerical investigations are performed for various values of Hartmann number and Rayleigh number. The obtained results are depicted in terms of streamlines and isotherms which show the significant effects of Hartmann number on the fluid flow and temperature distribution inside the enclosure. Also, it was found that the Nusselt number decreases with an increase in the Hartmann number.

Blood flow in stenosed arteries with radially variable viscosity, peripheral plasma layer thickness and magnetic field

Abstract: A novel approach of combined mathematical and computational models has been developed to investigate the oscillatory two-layered flow of blood through arterial stenosis in the presence of a transverse uniform magnetic field applied Blood in the core region and plasma fluid in the peripheral layer region are assumed to obey the law of Newtonian fluid An analytical solution is obtained for velocity profile and volumetric flow rate in the peripheral plasma region and also wall shear stress Finite difference method is employed to solve the momentum equation for the core region The numerical solutions for velocity, flow rate and flow resistance are computed The effects of various parameters associated with the present flow problem such as radially variable viscosity, hematocrit, plasma layer thickness, magnetic field and pulsatile Reynolds number on the physiologically important flow characteristics namely velocity distribution, flow rate, wall shear stress and resistance to flow have been investigated It is observed that the velocity increases with the increase of plasma layer thickness An increase or a decrease in the velocity and wall shear stress against the increase in the value of magnetic parameter (Hartmann number) and hematocrit is dependent on the value of t An increase in magnetic field leads to an increase in the flow resistance and it decreases with the increase in the plasma layer thickness and pulsatile Reynolds number The information concerning the phase lag between the flow characteristics and how it is affected by the hematocrit, plasma layer thickness and Hartmann number has, for the first time, been added to the literature

Three-dimensional numerical simulations of magnetohydrodynamic flow around a confined circular cylinder under low, moderate, and strong magnetic fields

Abstract: This paper presents three-dimensional direct numerical simulations of liquid metal flow around a circular cylinder placed symmetrically in a rectangular duct, under a wide range of magnetic field intensities. Results are presented for values of the Hartmann number (based on the duct width) in the range of 0 ⩽ Ha ⩽ 1120, and the Reynolds number (based on the cylinder diameter and centerline velocity) in the range 0 ⩽ Rec ⩽ 5000. The generated flow regimes and the associated critical values of parameters are investigated in detail through full three-dimensional simulations. The effect of the magnetic field on the wake structure is discussed in relation to the possible mechanisms for the generation or suppression of vortices, and to previous attempts to model magnetohydrodynamic flows using simplified two-dimensional models. Present results reveal a non-monotonic dependance of the critical Reynolds number for the onset of vortex shedding, with respect to the Hartmann number. For certain combinations of Ha an...

Application of dtm on mhd jeffery hamel problem with nanoparticle

Abstract: In this paper, the MHD Jeffery Hamel problem with nanoparticles for various values of Hartmann number has been investigated. The present study discusses about the velocity profile in the steady 2-dimensional flow of a MHD fluid with nanoparticles between two nonparallel walls. At first a similarity transformation is used to reduce the partial differential equations modeling the flow, to a single third-order nonlinear differential equation containing the semi angle between the plates, Reynolds number, the magnetic field strength and nanoparticle volume fraction as parameters. Differential Transformation method (DTM) has been used in order to study the problem and finally the obtained analytical results have been compared with numerical solutions and results achieved from pervious works in some numerical cases.

Magnetoconvective Transport in a Vertical Lid-Driven Cavity Including a Heat Conducting Square Cylinder with Joule Heating

Abstract: The hydromagnetic mixed convection flow and heat transfer in a vertical lid-driven square enclosure is numerically simulated following a finite volume approach based on the SIMPLEC algorithm. Both the top and bottom horizontal walls of the enclosure are insulated, and the left and right vertical walls are kept isothermal with different temperatures. The left vertical wall is translating in its own plane at a uniform speed, while all other walls are stationary. Two cases of translational lid motion, viz. vertically upward and downward, are considered. A uniform magnetic field is applied along the horizontal direction normal to the translating wall. A heat conducting horizontal solid square cylinder is placed centrally within the outer enclosure. Simulations are conducted for various controlling parameters, such as the Richardson number (1 ≤ Ri ≤ 10), Hartmann number (0 ≤ Ha ≤ 50), and Joule heating parameter (0 ≤ J ≤ 5), keeping the Reynolds number based on lid velocity fixed as Re = 100. The flow and ther...