Showing papers on "Hartmann number published in 2009"

Approximate Analysis of MHD Squeeze Flow between Two Parallel Disks with Suction or Injection by Homotopy Perturbation Method

Abstract: An analysis has been performed to study magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid. We investigate the combined effect of inertia, electromagnetic forces, and suction or injection. With the introduction of a similarity transformation, the continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation. An approximate solution of the equation subject to the appropriate boundary conditions is derived using the homotopy perturbation method (HPM) and compared with the direct numerical solution (NS). Results showing the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the axial and radial velocity distributions are presented and discussed. The approximate solution is found to be highly accurate for the ranges of parameters investigated. Because of its simplicity, versatility and high accuracy, the method can be applied to study linear and nonlinear boundary value problems arising in other engineering applications.

Hall effects on MHD flow in a rotating system with heat transfer characteristics

Abstract: Closed-form solutions are derived for the steady magnetohydrodynamic (MHD) viscous flow in a parallel plate channel system with perfectly conducting walls in a rotating frame of reference, in the presence of Hall currents, heat transfer and a transverse uniform magnetic field A mathematical analysis is described to evaluate the velocity, induced magnetic field and mass flow rate distributions, for a wide range of the governing parameters Asymptotic behavior of the solution is analyzed for large M 2 (Hartmann number squared) and K 2 (rotation parameter) The heat transfer aspect is considered also with Joule and viscous heating effects present Boundary layers arise close to the channel walls for large K 2, ie strong rotation of the channel For slowly rotating systems (small K 2), Hall current parameter (m) reduces primary mass flow rate (Q x /R ρ v) Heat transfer rate at the upper plate (d θ/d η) η=1 decreases, while at the lower plate (d θ/d η) η=−1 increases, with increase in either K 2 or m For constant values of the rotation parameter, K 2, heat transfer rate at both plates exhibits an oscillatory pattern with an increase in Hall current parameter, m The response of the primary and secondary velocity components and also the primary and secondary induced magnetic field components to the control parameters is also studied graphically Applications of the study arise in rotating MHD induction machine energy generators, planetary and solar plasma fluid dynamics systems, magnetic field control of materials processing systems, hybrid magnetic propulsion systems for space travel etc

The effect of thermal radiation on the flow of a second grade fluid

Abstract: This paper reports the magnetohydrodynamic (MHD) flow and heat transfer characteristics of a second grade fluid in a channel. Analytic technique namely the homotopy analysis method (HAM) is used to solve the momentum and energy equations. The important findings in this paper are the effects of second grade parameter, Hartmann number, Reynolds number, thermal radiation parameter, Prandtl and local Eckert numbers on the velocity, temperature, skin friction coefficient and Nusselt number.

MHD duct flows under hydrodynamic “slip” condition

Abstract: Three classic MHD problems are revisited assuming hydrodynamic slip condition at the interface between the electrically conducting fluid and the insulating wall: (1) Hartmann flow; (2) fully developed flow in a rectangular duct; and (3) quasi-two-dimensional (Q2D) turbulent flow. The first two problems have been solved analytically. Additionally to the Hartmann number (Ha), a new dimensionless parameter S, the ratio of the slip length to the thickness of the Hartmann layer, has been identified. One of the most important conclusions of the paper is that the duct flows with the slip still exhibit Hartmann layers, whose thickness scales as 1/Ha, while the thickness of the side layers is a function of both Ha and S. In the case of Q2D flows, a new expression for the Hartmann braking time has been derived showing its increase at Ha >> 1 by factor (1+ S). Numerical simulations performed for a flow with the “M-shaped” velocity profile show that in the presence of the slip, a Q2D flow becomes more irregular as vortical structures experience less Joule and viscous dissipation in the Hartmann layers.

Linear stability of Hunt's flow

Abstract: We analyse numerically the linear stability of the fully developed flow of a liquid metal in a rectangular duct subject to a transverse magnetic field. The walls of the duct perpendicular to the magnetic field are perfectly conducting whereas the parallel ones are insulating. In a sufficiently strong magnetic field, the flow consists of two jets at the insulating walls and a near-stagnant core. We use a vector stream function formulation and Chebyshev collocation method to solve the eigenvalue problem for small-amplitude perturbations. Due to the two-fold reflection symmetry of the base flow the disturbances with four different parity combinations over the duct cross-section decouple from each other. Magnetic field renders the flow in a square duct linearly unstable at the Hartmann number Ha 5.7 with respect to a disturbance whose vorticity component along the magnetic field is even across the field and odd along it. For this mode, the minimum of the critical Reynolds number Re_c 2018, based on the maximal velocity, is attained at Ha ~ 10. Further increase of the magnetic field stabilises this mode with Re_c growing approximately as Ha. For Ha>40, the spanwise parity of the most dangerous disturbance reverses across the magnetic field. At Ha ~ 46 a new pair of most dangerous disturbances appears with the parity along the magnetic field being opposite to that of the previous two modes. The critical Reynolds number, which is very close for both of these modes, attains a minimum Re_c ~ 1130 at Ha ~ 70 and increases as Re_c ~ Ha^1/2 for Ha >> 1. The asymptotics of the critical wavenumber is k_c ~ 0.525Ha^1/2 while the critical phase velocity approaches 0.475 of the maximum jet velocity.

The velocity profile of laminar MHD flows in circular conducting pipes

Abstract: We present numerical simulations without modeling of an incompressible, laminar, unidirectional circular pipe flow of an electrically conducting fluid under the influence of a uniform transverse magnetic field. Our computations are performed using a finite-volume code that uses a charge-conserving formulation [called current-conservative formulation in references (Ni et al J Comput Phys 221(1):174–204, 2007, Ni et al J Comput Phys 227(1):205–228, 2007)]. Using high resolution unstructured meshes, we consider Hartmann numbers up to 3000 and various values of the wall conductance ratio c. In the limit $${c{\ll}{\rm Ha}^{-1}}$$ (insulating wall), our results are in excellent agreement with the so-called asymptotic solution (Shercliff J Fluid Mech 1:644–666, 1956). For higher values of the wall conductance ratio, a discrepancy with the asymptotic solution is observed and we exhibit regions of velocity overspeed in the Roberts layers. We characterise these overspeed regions as a function of the wall conductance ratio and the Hartmann number; a set of scaling laws is derived that is coherent with existing asymptotic analysis.

MHD Flow and Heat Transfer over a Stretching Sheet

Abstract: An analysis is made for the steady two-dimensional, laminar boundary layer flow of a viscous, incompressible, electrically conducting fluid near a stagnation point of stretching sheet in the presence of a magnetic field. It is assumed that the sheet is stretched in its own plane with velocity and temperature proportional to the distance from the stagnation point. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity variables. The solutions of momentum and energy equations have been obtained independently by a perturbation technique for a small magnetic parameter. The effects of the various parameters such as velocity parameter, Hartmann number, Prandtl number and Eckert number for velocity and temperature distributions have been discussed in detail with graphical representation.

Peristaltic transport and heat transfer of a MHD Newtonian fluid with variable viscosity

Abstract: The influence of temperature-dependent viscosity and magnetic field on the peristaltic flow of an incompressible, viscous Newtonian fluid is investigated. The governing equations are derived under the assumptions of long wavelength approximation. A regular perturbation expansion method is used to obtain the analytical solutions for the velocity and temperature fields. The expressions for the pressure rise, friction force and the relation between the flow rate and pressure gradient are obtain. In addition to analytical solutions, numerical results are also computed and compared with the analytical results with good agreement. The results are plotted for different values of variable viscosity parameter β, Hartmann number M, and amplitude ratio o. It is found that the pressure rise decreases as the viscosity parameter β increases and it increases as the Hartmann number M increases. Finally, the maximum pressure rise (σ=0) increases as M increases and β decreases.

On Temporal Stability Analysis for Hydromagnetic Flow in a Channel Filled with a Saturated Porous Medium

Abstract: In this paper, a linear stability analysis is presented to trace the time evolution of an infinitesimal, two-dimensional disturbance imposed on the base flow of an electrically conducting fluid in a channel filled with a saturated porous medium under the influence of a transversely imposed magnetic field. An eigenvalue problem is obtained and solved numerically using the Chebyshev collocation spectral method. The critical Reynolds number Re c, the critical wave number α c and the critical wave speed c c are obtained for a wide range of the porous medium shape factor parameter S and Hartmann number H. It is found that an increase in the magnetic field intensity and a decrease in porous medium permeability have a stabilizing effect on the fluid flow.

Homotopy analysis method for fully developed MHD micropolar fluid flow between vertical porous plates

Abstract: In this paper, the fully developed natural convection of MHD micropolar fluid flow between two vertical porous plates is considered. The coupled system of non-linear differential equations governing the flow is solved analytically by the homotopy analysis method (HAM). The HAM contains an auxiliary parameter ℏ, which provides us with a simple way to adjust and control the convergence region and rate of convergence of the series solution. Velocity, microrotation and temperature profiles are presented for several values of the Hartmann number and the micropolar parameter. Copyright © 2008 John Wiley & Sons, Ltd.

Lattice BGK simulations of double diffusive natural convection in a rectangular enclosure in the presences of magnetic field and heat source

Abstract: In this paper, we develop a temperature-concentration lattice Bhatnagar-Gross-Krook (TCLBGK) model, with a robust boundary scheme for simulating the two-dimensional, hydromagnetic, double-diffusive convective flow of a binary gas mixture in a rectangular enclosure, in which the upper and lower walls are insulated, while the left and right walls are at a constant temperature and concentration and a uniform magnetic field is applied in the x -direction. In the model, the velocity, temperature and concentration fields are solved by three independent LBGK equations which are combined into a coupled equation for the whole system. In our simulations, we take the Prandtl number P r = 1 , the Lewis number L e = 2 , the thermal Rayleigh number R a T = 10 5 , 10 6 , the Hartmann number H a = 0 , 10 , 25 , 50 , the dimensionless heat generation or absorption ϕ = 0.0 , − 1.0 , the buoyancy ratio N = 0.8 , 1.3 , and the aspect ratio A = 2 for the enclosure. The numerical results are found to be in good agreement with those of previous studies [A.J. Chamkha, H. Al-Naser, Hydromagnetic double-diffusive convection in a rectangular enclosure with opposing temperature and concentration gradients, Int. J. Heat Mass Transfer 45 (2002) 2465C2483].

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

Abstract: The nonaxisymmetric 'kink-type' Tayler instability (TI) of toroidal magnetic fields is studied for conducting incompressible fluids of uniform density between two infinitely long cylinders rotating around the same axis. It is shown that for resting cylinders the critical Hartmann number for the unstable modes does not depend on Pm. By rigid rotation the instability is suppressed where the critical ratio of the rotation velocity and the Alfven velocity of the field (only) slightly depends on the magnetic Prandtl number Pm. For Pm=1 the rotational quenching of TI takes its maximum. Rotation laws with negative shear (i.e. d\Omega/dR<0) strongly destabilize the toroidal field if the rotation is not too fast. For sufficiently high Reynolds numbers of rotation the suppression of the nonaxisymmetric magnetic instability always dominates. 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. For negative shear the Maxwell stress of the perturbations remarkably contributes to the angular momentum transport. 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 kAmp.

Soret effects due to natural convection between inclined plates with magnetic field

Abstract: The effect of small uniform magnetic field on separation of a binary mixture for the case of a fully developed natural convection between two heated inclined plates has been investigated in this paper. Neglecting the induced electric field the equations governing the motion, temperature and concentration are solved by simple perturbation technique, in terms of dimensionless parameter measuring buoyancy force. The expressions for velocity, temperature and concentration are obtained. The effects of Hartmann number (M), thermal diffusion number (td), the buoyancy force parameter (N) and the inclination angle (ψ) of the plates with the horizontal are studied on the flow and heat transfer quantities.

Dynamic stiffness and damping characteristics of one-dimensional magneto-hydrodynamic inclined-plane slider bearings:

Abstract: Considering the transient squeezing motion, the magneto-hydrodynamic (MHD) steady and dynamic characteristics of one-dimensional slider bearings lubricated with an electrically conducting fluid in the consideration of a transverse magnetic field are numerically investigated. Using the MHD motion equations and, the continuity equation, we have derived a MHD dynamic Reynolds-type equation, which is applicable to slider bearings taking into account the squeezing effect ∂ h/ ∂ t, in which the general film-shape function is described by h=h(x, t). A closed-form solution for the pressure of an inclined-plane slider is obtained and applied to predict the MHD dynamic stiffness and damping characteristics of bearings. According to the results obtained, the application of externally applied magnetic fields signifies an apparent increase in the MHD steady film pressure. Comparing with the classical non-conducting-lubricant case, the applied magnetic-field effects characterized by the Hartmann number provide ...

Magnetohydrodynamics Mixed Convection Around a Heat Conducting Horizontal Circular Cylinder in a Rectangular Lid-driven Cavity with Joule Heating

Abstract: In the present paper, a study of magnetohydrodynamic (MHD) mixed convection around a heat conducting horizontal circular cylinder placed at the center of a rectangular cavity along with joule heating has been carried out. Steady state heat transfer by laminar mixed convection has been studied numerically by solving the equations of mass, momentum and energy to determine the fluid flow and heat transfer characteristics in the cavity as a function of Richardson number, Hartmann number and the cavity aspect ratio. The results are presented in the form of average Nusselt number at the heated surface; average fluid temperature in the cavity and temperature at the cylinder center for the range of Richardson number, Hartmann number and aspect ratio. The streamlines and isotherms are also presented. It is found that the streamlines, isotherms, average Nusselt number, average fluid temperature and dimensionless temperature at the cylinder center strongly depend on the Richardson number, Hartmann number and the cavity aspect ratio. Keywords : Mixed convection; Finite element method; Cylinder diameter; Lid-driven cavity; Hartmann number. © 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i3.2597 J. Sci. Res. 1 (3), 461-472 (2009)

Magnetohydrodynamic viscous flow in a rotating porous medum cylindrical annulus with an applied radial magnetic field

Abstract: We study the steady, axisymmetric, magnetohydrodynamic (MHD) flow of a viscous, Newtonian, incompressible, electrically-conducting fluid through an isotropic, homogenous porous medium located in the annular zone between two concentric rotating cylinders in the presence of a radial magnetic field. Transformation variables are introduced to render the tangential and axial momentum equations non-dimensional with corresponding no-slip boundary conditions. Closed-form solutions are obtained using Bessel and Lommel functions. Axial velocity ( UZ) is found to decrease markedly with an increase in Hartmann number ( Ha ) with radial coordinate, with profiles becoming increasingly curved for stronger magnetic field. An approximately linear decay in axial velocity from the inner cylinder to the outer cylinder is computed for the non-magnetic case ( Ha = 0). Dimensionless tangential velocity ( Uθ) is also suppressed with magnetic field increasing; however profiles increase consistently from the inner cylinder to the outer cylinder i.e. over the domain 0.5 ≤R ≤ 1. Again for the electrically non-conducting case, the tangential velocity distribution is approximately linear. An increase in relative rotation parameter, N, which embodies the relative speeds of rotation of the inner to the outer cylinders (= b 2 1 ω ω ) strongly boosts the tangential velocity (Uθ) throughout the annular regime, in particular at the interior wall of the annulus ( R = 0.5). Increasing Darcy number induces a strong acceleration in both axial and tangential flow i.e. increases both components of velocity, although for low Da (= 0.01) there is a significant reversal in axial flow further from the inner wall of the annulus. An increase in axial pressure gradient induces a marked increase in the axial velocity component, ( Uz). Applications of the analysis include magnetic field control of rotating annular filter porous media membrane systems, drilling flows in geothermal operations, MHD power generators, geophysical hydromagnetics and fundamental magnetofluid dynamic studies.

Computation of MHD flow due to moving boundaries

Abstract: A non-iterative numerical scheme is presented which computes in a single iteration the steady, laminar flow of a viscous, incompressible, electrically conducting fluid caused by moving boundaries in the presence of a transverse magnetic field. It also eliminates the possible error induced by taking the value of numerical infinity (representing the unbounded domain of the flow) as a finite number. The scheme is based on implicit use of infinite series of exponentials for velocity components. The issue of convergence of these series is also discussed. An asymptotic solution valid for large values of M, the Hartmann number, and an approximate solution valid for any value of M are further developed. In particular, the case of axisymmetric magnetohydrodynamic (MHD) flow due to a stretching sheet has been dealt with in some detail. A comparison has been made of the merits of various techniques used in the paper and appropriate conclusions are drawn.