Showing papers on "Hartmann number published in 2011"

Effects of magnetic field on nanofluid forced convection in a partially heated microchannel

Abstract: This paper numerically examines the laminar forced convection of a water–Al 2 O 3 nanofluid flowing through a horizontal microchannel. The middle section of the microchannel is heated with a constant and uniform heat flux. The middle section is also influenced by a transverse magnetic field with a uniform strength. The effects of pertinent parameters such as the Reynolds number (0≤ Re ≤1000), the solid volume fraction (0≤ ϕ ≤0.04) and the Hartmann number (0≤ Ha ≤100) on the flow and temperature fields and the heat transfer performance of the microchannel are examined against numerical predictions. The results show that the microchannel performs better heat transfers at higher values of the Reynolds and Hartmann numbers. For all values of the Reynolds and Hartmann numbers considered in this study, the average Nusselt number on the middle section surface of the microchannel increases as the solid volume fraction increases. The rate of this increase is considerably more at higher values of the Reynolds number and at lower values of the Hartmann number.

Magnetoconvection in a Square Enclosure with Sinusoidal Temperature Distributions on Both Side Walls

Abstract: A computational study of convective flow and heat transfer in a cavity in the presence of uniform magnetic field is carried out. The side walls of the cavity have spatially varying sinusoidal temperature distributions. The horizontal walls are adiabatic. The governing equations are solved by the finite volume method. The results are discussed for different combinations of phase deviation, amplitude ratio, and Hartmann and Rayleigh numbers. It is observed that the heat transfer rate is increased with amplitude ratio. The heat transfer rate is increased first and then decreased on increasing the phase deviation. It is also found that the heat transfer rate is decreased with an increasing Hartmann number.

Pulsatile flow and heat transfer of a magneto-micropolar fluid through a stenosed artery under the influence of body acceleration

Abstract: With an aim to investigate the effect of externally imposed body acceleration and magnetic field on pulsatile flow of blood through an arterial segment having stenosis is under consideration in this article. The flow of blood is presented by an unsteady micropolar fluid, and the heat-transfer characteristics have been taken into account. The nonlinear equations that govern the flow are solved numerically using finite difference technique by employing a suitable coordinate transformation. The numerical results have been observed for axial and microrotation component of velocity, fluid acceleration, wall shear stress (WSS), flow resistance, temperature, and the volumetric flow rate. It thus turns out that the rate of heat transfer increases with the increase of Hartmann number H, while the WSS has a reducing effect on the Hartmann number H and an enhancing effect on the ratio of viscosity K as well as on the constriction height δ.

FDM analysis for MHD flow of a non-Newtonian fluid for blood flow in stenosed arteries

Abstract: A computational model is developed to analyze the effects of magnetic field in a pulsatile flow of blood through narrow arteries with mild stenosis, treating blood as Casson fluid model. Finite difference method is employed to solve the simplified nonlinear partial differential equation and an explicit finite difference scheme is obtained for velocity and subsequently the finite difference formula for the flow rate, skin friction and longitudinal impedance are also derived. The effects of various parameters associated with this flow problem such as stenosis height, yield stress, magnetic field and amplitude of the pressure gradient on the physiologically important flow quantities namely velocity distribution, flow rate, skin friction and longitudinal impedance to flow are analyzed by plotting the graphs for the variation of these flow quantities for different values of the aforesaid parameters. It is found that the velocity and flow rate decrease with the increase of the Hartmann number and the reverse behavior is noticed for the wall shear stress and longitudinal impedance of the flow. It is noted that flow rate increases and skin friction decreases with the increase of the pressure gradient. It is also observed that the skin friction and longitudinal impedance increase with the increase of the amplitude parameter of the artery radius. It is also found that the skin friction and longitudinal impedance increases with the increase of the stenosis depth. It is recorded that the estimates of the increase in the skin friction and longitudinal impedance to flow increase considerably with the increase of the Hartmann number.

A numerical model for the magnetohydrodynamic flow of blood in a porous channel

Abstract: Magnetohydrodynamic (MHD) principles may be used to study the flow of arterial blood under the action of an applied magnetic field. Such studies are of potential value in the treatment of cardiovascular disorders that may be associated with accelerated circulation. With an aim to providing a generalized model for studying the flow of blood in an electromagnetic field environment, a numerical model is developed here, by treating blood as a non-Newtonian fluid, the motion of which is taken to be governed by Walter's B-fluid model. The channel flow characteristics of the fluid are studied here, when the channel is porous and is subjected to an external magnetic field. Using the similarity transformation and boundary layer approximations, the associated nonlinear partial differential equations of the problem are reduced to nonlinear ordinary differential equations. These are solved numerically by developing a finite difference scheme. The study provides useful estimates for the influence of Reynolds number Re, Hartmann number M, and viscoelastic parameter K1 on the flow characteristics. It bears the potential to explore some important information about the hemodynamical flow of blood in an artery when it is under the action of an external magnetic field.

Instability of magnetohydrodynamic flow in an annular channel at high Hartmann number

Abstract: Instability of a flow of an electrically conducting fluid in an annular channel is analyzed. Strong constant magnetic field is imposed in the axial direction. Similarly to toroidal duct experiments, the flow is driven by the azimuthal Lorentz force resulting from the interaction between the magnetic field and the radial electric currents created by a difference of electric potential imposed between the cylinders. The instability of the base flow, while clearly of centrifugal nature, is significantly different from the Dean instability detected earlier in hydrodynamic systems and similar MHD systems at low and moderate magnetic fields. Growing perturbations are oscillating and axisymmetric and consist of counter-rotating toroidal vortices arranged side by side in the radial direction and having meridional cross-sections in the form of elongated ellipses oriented slightly obliquely to the axial direction. Simulations of the secondary flow show an interesting feature of periodic transitions between two symmetric solutions.

Streaming-potential phenomena in the thin-Debye-layer limit. Part 1. General theory

Abstract: Electrokinetic streaming-potential phenomena are driven by imposed relative motion between liquid electrolytes and charged solids. Owing to non-uniform convective ‘surface’ current within the Debye layer Ohmic currents from the electro-neutral bulk are required to ensure charge conservation thereby inducing a bulk electric field. This, in turn, results in electro-viscous drag enhancement. The appropriate modelling of these phenomena in the limit of thin Debye layers ( denoting the dimensionless Debye thickness) has been a matter of ongoing controversy apparently settled by Cox’s seminal analysis (J. Fluid Mech., vol. 338, 1997, p. 1). This analysis predicts electro-viscous forces that scale as resulting from the perturbation of the original Stokes flow with the Maxwell-stress contribution only appearing at higher orders. Using scaling analysis we clarify the distinction between the normalizations pertinent to field- and motion-driven electrokinetic phenomena, respectively. In the latter class we demonstrate that the product of the Hartmann & Peclet numbers is contrary to Cox (1997) where both parameters are assumed . We focus on the case where motion-induced fields are comparable to the thermal scale and accordingly present a singular-perturbation analysis for the limit where the Hartmann number is and the Peclet number is . Electric-current matching between the Debye layer and the electro-neutral bulk provides an inhomogeneous Neumann condition governing the electric field in the latter. This field, in turn, results in a velocity perturbation generated by a Smoluchowski-type slip condition. Owing to the dominant convection, the present analysis yields an asymptotic structure considerably simpler than that of Cox (1997): the electro-viscous effect now already appears at and is contributed by both Maxwell and viscous stresses. The present paradigm is illustrated for the prototypic problem of a sphere sedimenting in an unbounded fluid domain with the resulting drag correction differing from that calculated by Cox (1997). Independently of current matching, salt-flux matching between the Debye layer and the bulk domain needs also to be satisfied. This subtle point has apparently gone unnoticed in the literature, perhaps because it is trivially satisfied in field-driven problems. In the present limit this requirement seems incompatible with the uniform salt distribution in the convection-dominated bulk domain. This paradox is resolved by identifying the dual singularity associated with the limit in motion-driven problems resulting in a diffusive layer of thickness beyond the familiar -wide Debye layer.

Effects of magnetic field, porosity, and wall properties for anisotropically elastic multi-stenosis arteries on blood flow characteristics

Abstract: A mathematical model for blood flow through an elastic artery with multistenosis under the effect of a magnetic field in a porous medium is presented The considered arterial segment is simulated by an anisotropically elastic cylindrical tube filled with a viscous incompressible electrically conducting fluid representing blood An artery with mild local narrowing in its lumen forming a stenosis is analyzed The effects of arterial wall parameters represent viscoelastic stresses along the longitudinal and circumferential directions T t and T θ , respectively The degree of anisotropy of the vessel wall γ, total mass of the vessel, and surrounding tissues M and contributions of the viscous and elastic constraints to the total tethering C and K respectively on resistance impedance, wall shear stress distribution, and radial and axial velocities are illustrated Also, the effects of the stenosis shape m, the constant of permeability X, the Hartmann number H α and the maximum height of the stenosis size δ on the fluid flow characteristics are investigated The results show that the flow is appreciably influenced by surrounding connective tissues of the arterial wall motion, and the degree of anisotropy of the vessel wall plays an important role in determining the material of the artery Further, the wall shear stress distribution increases with increasing T t and γ while decreases with increasing T θ , M, C, and K Transmission of the wall shear stress distribution and resistance impedance at the wall surface through a tethered tube are substantially lower than those through a free tube, while the shearing stress distribution at the stenosis throat has inverse characteristic through totally tethered and free tubes The trapping bolus increases in size toward the line center of the tube as the permeability constant X increases and decreases with the Hartmann number Ha increased Finally, the trapping bolus appears, gradually in the case of non-symmetric stenosis, and disappears in the case of symmetric stenosis The size of trapped bolus for the stream lines in a free isotropic tube (ie, a tube initially unstressed) is smaller than those in a tethered tube

Analysis of the flow and heat transfer characteristics for MHD free convection in an enclosure with a heated obstacle

Abstract: Finite element method based on Galerkin weighted Residual approach is used to solve two-dimensional governing mass, momentum and energy equations for steady state, natural convection flow in presence of magnetic field inside a square enclosure. The cavity consists of three adiabatic walls and one constantly heated wall. A uniformly heated circular solid body is located at the centre of the enclosure. The aim of this study is to describe the effects of MHD on the flow and thermal fields in presence of such heated obstacle. The investigations are conducted for different values of Rayleigh number (Ra) and Hartmann number (Ha). Various characteristics of streamlines, isotherms and heat transfer rate in terms of the average Nusselt number (Nu) are presented for different parameters. The effect of physical parameter (D) is also shown here. The results indicate that the flow pattern and temperature field are significantly dependent on the above mentioned parameters.

Flow and Heat Transfer of Two Immiscible Fluids in the Presence of Uniform Inclined Magnetic Field

Abstract: The magnetohydrodynamic (MHD) Couette flow of two immiscible fluids in a horizontal channel with isothermal walls in the presence of an applied electric and inclined magnetic field has been investigated in the paper. Both fluids are electrically conducting, while the channel plates are electrically insulated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ordinary differential equations, and closed-form solutions are obtained in both fluid regions of the channel. Separate solutions with appropriate boundary conditions for each fluid have been obtained, and these solutions have been matched at the interface using suitable matching conditions. The analytical results for various values of the Hartmann number, the angle of magnetic field inclination, loading parameter, and the ratio of fluid heights have been presented graphically to show their effect on the flow and heat transfer characteristics.

Influence of an axial magnetic field on the stability of spherical Couette flows with different gap widths

Abstract: This paper deals with the linear instability analysis of the spherical Couette flow of an electrically conducting fluid in the presence of an axial magnetic field. The numerical investigations are performed for different ratios, η = 0.5 and η = 0.6, and compared with Hollerbach’s work for η = 0.33 (Hollerbach in Proc R Soc 465:2003, 2009). The corresponding instability diagrams, i.e., the critical values of the Reynolds number Re, the wave number, and the frequency on the Hartmann number Ha, are presented and accompanied by simulation of the transition between three-dimensional flow states of different symmetries. The characteristic subdivision of the linear stability curves into anti-symmetric modes, which is responsible for the instability at small Ha, and symmetric modes occurring at higher Ha is found for larger η, too. However, the extension of the stability corridor between the anti-symmetric and the symmetric modes increases nonlinearly with η. This offers the possibility to stabilize the basic flow up to high Re by appropriately increasing Ha.

Unsteady Magnetohydrodynamic Heat Transfer in a Semi-Infinite Porous Medium with Thermal Radiation Flux: Analytical and Numerical Study

Abstract: The unsteady, buoyancy-induced, hydromagnetic, thermal convection flow in a semi-infinite porous regime adjacent to an infinite hot vertical plate moving with constant velocity, is studied in the presence of significant thermal radiation. The momentum and energy conservation equations are normalized and then solved using both the Laplace transform technique and Network Numerical Simulation. Excellent agreement is obtained between both analytical and numerical methods. An increase in Hartmann number (𝑀2) strongly decelerates the flow and for very high strength magnetic fields (𝑀2=20), the flow is reversed after a short time interval. The classical velocity overshoot is also detected close to the plate surface for low to intermediate values of 𝑀2 at both small and large times; however this overshoot vanishes for larger strengths of the transverse magnetic field (𝑀2=10). An increase in radiation-conduction parameter (𝐾𝑟) significantly increases temperature throughout the porous regime at both small and larger times, adjacent to the plate, but decreases the shear stress magnitudes at the plate. Temperature gradient is reduced at the plate surface for all times, with a rise in radiation-conduction parameter (𝐾𝑟). Shear stress is reduced considerably with an increase in Darcian drag parameter (𝐾𝑝).

Numerical simulation of double-diffusive natural convective flow in an inclined rectangular enclosure in the presence of magnetic field and heat source, part A: Effect of Rayleigh number and inclination angle

Abstract: Double-diffusive convective flow in an inclined rectangular enclosure with the shortest sides being insulated and impermeable is investigated numerically. Constant temperatures and concentration are imposed along the longest sides of the enclosure. In addition, a uniform magnetic field is applied in a horizontal direction. Laminar regime is considered under steady state condition. The transport equations for continuity, momentum, energy and species transfer are solved using the finite volume technique. The validity of the numerical code used is ascertained and good agreement was found with published results. The numerical results are reported for the effect of thermal Rayleigh number on the contours of streamline, temperature, and concentration. In addition, results for the average Nusselt and Sherwood numbers are presented and discussed for various parametric conditions. This study was done for constant Prandtl number, Pr = 0.7, aspect ratio, A = 2, Lewis number, Le = 2, the buoyancy ratio, N = 1, Hartmann number, Ha = 10 and the dimensionless heat generation, Φ = 1. Computations are carried out for RaT ranging from 103 to 5 * 105 and inclination angle range of 0° ⩽ γ ⩽ 180°.

Induced magnetic field with radiating fluid over a porous vertical plate: analytical study

Abstract: The objective of this investigation is to study the influence of thermal radiation and magnetic Prandtl number on the steady MHD heat and mass transfer by mixed convection flow of a viscous, incompressible, electrically-conducting, Newtonian fluid which is an optically thin gray gas over a vertical porous plate taking into account the induced magnetic field. The similarity solutions of the transformed dimensionless governing equations are obtained by series solution. It is found that, velocity is reduced considerably with a rise in conduction-radiation parameter ( R ) or Hartmann number ( M ) whereas the skin friction is found to be markedly boosted with an increase in M or Magnetic Prandtl number ( Pm ) . An increase in magnetic body parameter ( M ) or Magnetic Prandtl number ( Pm ) is found to escalate induced magnetic field whereas an increase in R is shown to exert the opposite effect. Applications of the study include laminar magneto-aerodynamics, materials processing and MHD propulsion thermo-fluid dynamics. DOI: 10.3329/jname.v7i2.5662

Quasi-two-dimensional convection in a three-dimensional laterally heated box in a strong magnetic field normal to main circulation

Abstract: Convection in a laterally heated three-dimensional box affected by a strong magnetic field is considered in the quasi-two-dimensional (Q2D) formulation. It is assumed that the magnetic field is strong and is normal to the main convective circulation. The stability of the resulting Q2D flow is studied for two values of the Hartmann number scaled by half of the width ratio, 100 and 1000, and for either thermally insulating or perfectly conducting horizontal boundaries. The aspect length-to-height ratio of the box is varied continuously between 4 and 10. It is shown that the magnetic field damps the bulk flow and creates thermal and Shercliff boundary layers at the boundaries, which become the main source of instabilities. In spite of the general tendency of the flow stabilization by the magnetic field, the flow instability takes place in different ways depending on the boundary conditions and the aspect ratio. Similarities with other magnetic field directions and flows with larger Prandtl numbers are discussed.

Unsteady Heat Transfer to MHD Oscillatory Flow through a Porous Medium under Slip Condition

Abstract: In this paper, we investigate the effects of slip condition, transverse magnetic field and radiative heat transfer to unsteady flow of a conducting optically thin fluid through a channel filled with porous medium. Exact solution of the governing equations for fully developed flow is obtained in closed form. Detailed computations of the influence of the Grashof number, Hartmann number, slip parameter, porosity parameter, radiation parameter and frequency of the oscillation are discussed.

A Tailored Finite Point Method for Solving Steady MHD Duct Flow Problems with Boundary Layers

Abstract: In this paper we propose a development of the finite difference method, called the tailored finite point method, for solving steady magnetohydrodynamic (MHD) duct flow problems with a high Hartmann number. When the Hartmann number is large, the MHD duct flow is convection-dominated and thus its solution may exhibit localized phenomena such as the boundary layer. Most conventional numerical methods can not efficiently solve the layer problem because they are lacking in either stability or accuracy. However, the proposed tailored finite point method is capable of resolving high gradients near the layer regions without refining the mesh. Firstly, we devise the tailored finite point method for the scalar inhomogeneous convection-diffusion problem, and then extend it to the MHD duct flow which consists of a coupled system of convection-diffusion equations. For each interior grid point of a given rectangular mesh, we construct a finite-point difference operator at that point with some nearby grid points, where the coefficients of the difference operator are tailored to some particular properties of the problem. Numerical examples are provided to show the high performance of the proposed method.