Showing papers on "Hartmann number published in 1998"

Numerical study of laminar natural convection in tilted enclosure with transverse magnetic field

Abstract: This paper numerically investigates the effect of the transverse magnetic field on flow field patterns and heat transfer processes in a tilted square cavity. The horizontal walls of the enclosure are assumed to be insulated while the vertical walls are kept isothermal. The power law control volume approach is developed to solve the conservation equations at Prandtl number of 0.71. Validation tests with existing data demonstrate the ability of the present scheme to produce accurate results. The effects of Grashof number, enclosure inclination angle, and Hartmann number are also investigated. The study covers the range of the Hartmann number from 0 to 100, the enclosure inclination angle from 0° to ‐90° with Grashof number of 104 and 106. The effect of the magnetic field is found to suppress the convection currents and heat transfer inside the cavity. This effect is significant for low inclination angles and high Grashof numbers. Additionally, it is noted that there is no variation of average Nusselt number with respect to inclination angle for high Hartmann number.

Hydromagnetic Natural Convection from AN Inclined Porous Square Enclosure with Heat Generation

Abstract: The problem of unsteady, laminar, two-dimensional hydromagnetic natural convection heat transfer in an inclined square enclosure filled with a fluid-saturated porous medium in the presence of a transverse magnetic field and fluid heat generation effects is studied numerically. The walls of the enclosure are maintained at constant temperatures. The flow in the porous region is modeled using the Brinkman-extended Darcy's law to account for the no-slip conditions at the walls. The control volume method is used to solve the governing balance equations for different values of the Darcy number, Hartmann number, and the inclination angle. Favorable comparisons with previously published work are performed. These comparisons confirmed the correctness of the numerical results. The obtained numerical results are presented graphically in terms of streamlines and isotherms as well as velocity and temperature profiles at midsections of the cavity to illustrate interesting features of the solution.

The effect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous media

Abstract: The effect of uniform suction/blowing on steady two-dimensional laminar forced MHD Hiemenz flow against a flat plate with variable wall temperature in a porous medium is numerically analyzed. The nonlinear boundary-layer equation were transformed and the resulting ordinary differential equations were solved by Keller box method. Numerical results for the dimensionless velocity profiles, the temperature profiles, the local friction coefficient and the local Nusselt number are presented for various values of Prandtl number Pr, the Hartmann number M, exponent of wall temperature λ, the permeability parameter Ω, and suction/blowing parameterf w . Generally, it has been found that the local friction coefficient and the local Nusselt number increase owing to suction of fluid and increasing Ω. This trend reversed for blowing of fluid and decreasing Ω. The type of flow is from pure fluid flow for Ω is very small changed into pure Darcy flow for Ω is very large.

Enhanced heat transfer rate measured for natural convection in liquid gallium in a cubical enclosure under a static magnetic field

Abstract: The heat transfer rate of natural convection in liquid gallium in a cubical enclosure was measured experimentally under an external magnetic field applied horizontally and parallel to the vertical heated wall and the opposing cooled wall of the enclosure. One vertical wall was heated with an electric heater and the opposing wall was cooled isothermally with running water. Experiments were conducted in the range of modified Rayleigh number from 1.85 x 10 6 to 4.76 x 10 6 and of Hartmann number from 0 to 573

Effect of a rotating magnetic field of arbitrary frequency on a liquid metal column

Abstract: We consider the influence of a rotating magnetic field on an infinitely long cylindrical liquid metal column. A solution for the flow field and magnetic field distribution is obtained for any value of the Hartmann number, Ha, and of the shielding parameter, Rω. When Ha ⪢ 1, it has been shown that, as long as R ω Ha √2 , the flow consists of a core rotating with the same angular velocity as that of the magnetic field and of a Hartmann boundary layer at the wall. The flow also contains recirculating eddies which are aligned with the magnetic field in the cylinder core. It is noted that the magnetic field is swept by the convective effect of the flow in the wall boundary layer whereas it satisfies a pure diffusion regime in the core. A simplified ring model permits a simple explanation of the critical value R ω = Ha √2 .

Stability of hydromagnetic dissipative Couette flow with non-axisymmetric disturbance

Abstract: A linear stability analysis has been implemented for hydromagnetic dissipative Couette flow, a viscous electrically conducting fluid between rotating concentric cylinders in the presence of a uniform axial magnetic field. The small-gap equations with respect to non-axisymmetric disturbances are derived and solved by a direct numerical procedure. Both types of boundary conditions, conducting and non-conducting walls, are considered. A parametric study covering wide ranges of μ, the ratio of angular velocity of the outer cylinder to that of inner cylinder, and Q, the Hartmann number which represents the strength of axial magnetic field, is conducted. Results show that the stability characteristics depend on the conductivity of the cylinders. For the case of non-conducting walls, it is found that the critical disturbance is a non-axisymmetric mode as the value of μ is sufficiently negative and the domain of Q where non-axisymmetric instability modes prevail is limited. Similar results are obtained for conducting walls at low Hartmann number. In addition, the transition of the onset of instability from non-axisymmetric modes to axisymmetric modes for the case μ=−1 with increasing strength of magnetic field are discussed in detail. For high values of the Hartmann number, the critical disturbance is always the axisymmetric stationary mode for non-conducting walls but not for conducting walls. For −1[les ]μ<1, it is demonstrated that non-axisymmetric instability modes prevail in a wide range of Q for conducting walls and axisymmetric oscillatory modes may, in fact, become more critical than both of the non-axisymmetric and axisymmetric stationary modes at higher values of the Hartmann number.

Effect of Thermocapillarity on the Production of a Conducting Thin Film in the Presence of a Transverse Magnetic Field

Abstract: The gradual development of a thin liquid film on the surface of a rotating disk is studied analytically when the thermocapillary force is in action in the presence of a transverse magnetic field. It is found that the acting thermocapillary force has a profound effect in enhancing the thinning rate of the film even in the presence of large Hartmann number M. A physical explanation of this result is provided. Large amounts of fluid are depleted in a small span of time when the Hartmann number M is small.

Resistivity profile and instability of the plane sheet pinch

Abstract: The stability of the quiescent ground state of an incompressible, viscous and electrically conducting fluid sheet, bounded by stress-free parallel planes and driven by an external electric field tangential to the boundaries, is studied numerically. The electrical conductivity varies as cosh−2(x1/a), where x1 is the cross-sheet coordinate and a is the half width of a current layer centered about the midplane of the sheet. For a≲0.4L, where L is the distance between the boundary planes, the ground state is unstable to disturbances whose wavelengths parallel to the sheet lie between lower and upper bounds depending on the value of a and on the Hartmann number. Asymmetry of the configuration with respect to the midplane of the sheet, modelled by the addition of an externally imposed constant magnetic field to a symmetric equilibrium field, acts as a stabilizing factor.

Hydromagnetic stability of current-induced flow in a small gap between concentric rotating cylinders

Abstract: The stability analysis of the flow of a viscous electrically conducting fluid between concentric rotating cylinders in the presence of an axial magnetic field is extended to the case where the primary flow includes a pressure gradient acting in the azimuthal direction. The pressure gradient is produced electromagnetically by the interaction of a superimposed radial current and the uniform axial magnetic field. The assumption of small gap approximation is made and the governing equations with respect to both axisymmetric and non–axisymmetric three–dimensional disturbances are derived and solved by a direct numerical procedure. A parametric study covering wide ranges of Q , the Hartmann number which represents the strength of axial magnetic field, and β, a parameter characterizing the ratio of current induced and rotation velocities, is conducted for weakly conducting cylinders and the situation of practical interest where the outer cylinder is stationary and the inner cylinder is rotating. The area where the onset mode is non–axisymmetric is shown in the plane β, Q ). It is found that the most stable state occurs approximately along a critical curve (β + 4.3) Q 2 + 56250(β + 3.75) = 0 and the critical axial wavenumber always has discontinuity when the parameters Q and β cross this curve. The critical mode transition of the onset of instability will be demonstrated in detail and results for the critical wavenumber and the critical Taylor number are presented. The corresponding values of the radial current density required for the appearance of secondary flow are also determined.

Analytical Model of a Side-Heated Free Convection Loop Placed in a Transverse Magnetic Field

Abstract: The hydrodynamic characteristics of a buoyancy-driven convection loop containing an electrically-conducting fluid in a transverse magnetic field are investigated analytically using a one-dimensional model. One side of the loop is isothermally heated and the other side isothermally cooled, and the upper and lower sections are insulated. The model which is based on the use of the Hartmann Plane-Poiseuille flow solution for estimating loop shear stress, predicts the flow velocity and the induced current of the magnetohydrodynamic generator in terms of the flow and geometric parameters. The study covers ranges of Grashof number, Gr, from 102 to 106 , the Hartmann number, Ha, from 0 to 20, the Prandtl number, Pr, from .003 to 7, and loop height to thickness ratio, L/d, from 10 to 50. It is shown that at low Prandtl numbers, Pr ≪ 1, there exists an optimal Hartmann number, Haopt , that maximizes the induced electric current. This Haopt depends weakly on the Grashof number. The side-heated loop performance is also compared with the bottom heated loop model of Ghaddar, (1997a). It is found that at a low Prandtl number, side heated loop induces the higher velocity whereas at high Prandtl numbers the bottom heated loop induces higher velocity.

Numerical simulation of side‐heated free convection loop placed in transverse magnetic field; the induced electric current

Abstract: The hydrodynamic characteristic of a buoyancy‐driven convection loop containing an electrically‐conducting fluid in a transverse magnetic field is numerically investigated using a two‐dimensional spectral element numerical model. One side of the loop is heated isothermally, the other side is cooled isothermally and the top and bottom sections are insulated. The study covers ranges of Grashof number, Gr, from 103 to 105, the Hartmann number, Ha, from 0 to 20, loop height to thickness ratio, L/d, from 10 to 20 and at Prandtl numbers of Pr = 0.02 and Pr = 1. Results are presented for the velocity, temperature profiles and heat transfer in terms of Hartmann number. At high Hartmann numbers the velocity gradient in the core of the flow decreases outside the Hartmann layer in the vicinity of the walls normal to the magnetic field. Comparison is made with the analytical solution of Ghaddar (1997), based on a parallel flow approximation and its range of validity is delineated. The numerical analysis compares well with the closed form analytical solution of the magnetohydrodynamic generator for the flow velocity and the induced current. This study reveals the existence of an optimal Hartmann number at which the induced electric current is maximised for all ranges of Prandtl numbers. The optimal Hartmann number found numerically for Pr = 0.02 is similar to the one predicted by the analytical 1‐D model.

Nonlinear analysis on the natural convection between vertical plates in the presence of a horizontal magnetic field

Abstract: Finite-amplitude secondary motions of an electrically conducting fluid between two vertical parallel plates heated differntially in the presence of a horizontal magnetic field are obtained numerically in the limit of a small Prandtl number and a small magnetic Prandtl number. We find that, as in the purely hydrodynamic case with the Hartmann number H = 0 examined by Nagata and Busse (1983), the bifurcation of the secondary flows is supercritical at the critical Grashof number G = Gc when H is small. Subcritical bifurcations occur at higher wavenumbers. As H is increased, the occurrence of the subcritical bifurcations moves gradually towards a smaller wavenumber region along the neutral curve. For H = 10 subcritical motions dominate across the whole range of wavenumbers. The stability analysis shows that the stability of the supercritical motions for small H is bounded by an onset of monotonically growing instability at a higher Grashof number G = G2.c. The stability region (Gc H ⋍ 7 .

The stability of combined plane poiseuille and couette flow in the presence of a transverse magnetic field

Abstract: M. Takashima. Department of Physics, Faculty of Science, Osaka City University, Osaka 558, Japan. FAX: 06 6605-2532 Abstract: The stability of combined plane Poiseuille and Couette ow of an electrically conducting uid under a transverse magnetic þeld is investigated using linear stability theory. In deriving the equations governing the stability, the so-called magnetic Stokes approximation is made using the fact that the magnetic Prandtl number Prm for most electrically conducting uids is extremely small. The Chebyshev collocation method is adopted to obtain the eigenvalue equation, which is then solved numerically. The critical Reynolds number Rec, the critical wave number ac, and the critical wave speed cc are obtained for wide ranges of the Hartmann number Ha and the parameter k › U0U(U0 + v0), where U0 is the maximum velocity of pure Couette ow and v0 is the maximum velocity of pure Poiseuille ow. It is found that a transverse magnetic þeld has both stabilizing and destabilizing effects on the ow depending on the value of k.

Numerical simulation of two-dimensional unsteady magnetohydrodynamic duct flows

Abstract: Introduction Generalities F numerical simulations of inertial flows are often limited to the steady regime and are always limited to very low Hartmann numbers' (Ha ~ 50). The Hartmann number is related to the ratio between the electromagnetic and the viscous forces. It is therefore a measure of the magnetic field strength for a given fluid in a duct of a given scale. Magnetohydrodynamic (MHD) boundary layers can be much thinner than pure hydrodynamic layers. A boundary layer perpendicular to the magnetic field has its thickness scaled with Ha~. The thickness of a boundary layer parallel to the magnetic field scales with Ha~. Therefore, numerical simulations are limited by the resolution of the boundary layers at high Hartmann numbers.