Magnetic field effect on fluid flow characteristics in a pipe for laminar flow

The influence of a magnetic field on the skin friction factor of steady fully-developed laminar flow through a pipe was studied experimentally. A mathematical model was introduced and a finite difference scheme used to solve the governing equations in terms of vorticity-stream function. The model predictions agree favourably with experimental results. It is observed that the pressure drop varies in proportion to the square of the product of the magnetic field and the sine of the magnetic field angle. Also, the pressure drop is proportional to the flow rate. This situation is similar to what applies in the absence of a magnetic field. It is found that a transverse magnetic field changes the axial velocity profile from the parabolic to a relatively flat shape. At first, the radial velocity rises more rapidly and then gradually decreases along the pipe until falling to zero. A numerical correlation can be written for the considerable distance required for the new axial velocity profile to establish. Owing to the changes taking place in the axial velocity profile, it exhibits a higher skin friction factor. The new axial velocity profile asymptotically approaches its limit as the Hartmann number becomes large.     

Two -fluid nonlinear mathematical model for pulsatile blood flow through catheterized arteries

The pulsatile flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The resulting system of the nonlinear implicit system of partial differential equations is solved by perturbation method. The expressions for shear stress, velocity, flow rate, wall shear stress and longitudinal impedance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio, amplitude, pulsatile Reynolds number ratio and peripheral layer thickness are discussed. The velocity and flow rate are observed to decrease, and the wall shear stress and resistance to flow increase when the yield stress increases. The plug flow velocity and flow rate decrease, and the longitudinal impedance increases when the catheter radius ratio increases. The velocity and flow rate increase while the wall shear stress and longitudinal impedance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the longitudinal impedance are significantly lower for the present two-fluid model than those of the single-fluid model. This paper was recommended for publication in revised form by Associate Editor Gihun Son Dr. D. S. Sankar received his B. Sc degree in Mathematics from the University of Madras, India, in 1989. He then received his M.Sc, M. Phil and Ph.D. degrees from Anna University, India in 1991, 1992 and 2004, respectively. Dr. D. S. Sankar is currently working at the School of Mathematical Sciences, University Science Malaysia, Malaysia. He serves as a referee for several reputed international journals. Dr. D. S. Sankar’s research interests include Fluid Dynamics, Hemodynamics, Differential Equations and Numerical Analysis. Dr. Usik Lee received his B.S. degree in Mechanical Engineering from Yonsei University, Korea in 1979. He then received his M.S. and Ph.D. degrees in Mechanical Engineering from Stanford University, USA in 1982 and 1985, respectively. Dr. Lee is currently a Professor at the Department of Mechanical Engineering at Inha University in Incheon, Korea. He serves as a referee for many reputed international journals. Dr. Lee’s research interests include structural dynamics, biomechanics, and computational mechanics.     

Magnetic field effect on laminar heat transfer in a pipe for thermal entry region

The influence of a transverse magnetic field on the local heat transfer of an electrically-conducting laminar fluid flow with high Prandtl number through a pipe was studied experimentally. Experiments indicated an increase in the local Nusselt number. The coupled set of the equations of motion and the energy equation including the viscous and Joule dissipation terms becomes non-linear and is solved numerically using a finite difference scheme. Favorable comparisons with experimental results confirm the correctness of the numerical results. It is found that the influence of magnetic field can be diminished by reducing the angle between the flow direction and the direction of magnetic field. The wall temperature reduces as the value of Hartmann number increases and the reduction rate of the wall temperature decreases as the value of Hartmann number exceeds a certain value. The average Nusselt number asymptotically approaches its limit as the Hartmann number becomes larger. Also, curve fitting can be employed to derive an equation for the average Nusselt number as a function of the Hartmann number. This equation is similar to the Sieder-Tate equation. It is observed that increasing the Hartmann number has no considerable effect on the thermal boundary layer thickness but decreases the temperature of fluid layers inside the boundary layer.     

Unsteady magnetohydrodynamic couette flow

The effect of a uniform transverse magnetic field on the Couette flow of an electrically conducting fluid between two parallel plates for impulsive and uniformly accelerated motion of one of the plates is discussed. The magnetic lines of force are assumed to be fixed relative to the moving plate. The Laplace transform technique has been used to obtain the expressions for the velocity field and skin friction. The effect of the magnetic field is to increase the velocity field in both cases.     

The magnetohydrodynamic thrust bearing with variable film thickness

Thrust bearings with converging and diverging film thicknesses under external azimuthal magnetic fields are analysed. With constant flow rate and positive terminal potential difference load capacity diminishes to a minimum then increases with increase of Hartmann number. With negative terminal potential difference load capacity increases with increase of Hartmann number. Under short circuit conditions the load capacity increases with increase of Hartmann number. Load capacity is unaffected by magnetic field under an open circuit condition. For constant flow rate and Hartmann number load capacity increases with increase of current; current increases as the terminal potential difference diminishes.     

Fluctuating flow of a viscoelastic liquid between two parallel plates with time-varying suction

The non-steady flow of a viscoelastic liquid between two parallel porous plates was studied when the suction velocity normal to the plate oscillates in magnitude but not in direction about a non-zero constant mean and one plate is at rest and the other oscillates harmonically about a non-zero constant mean. The response of skin friction to fluctuating flow and suction velocity was studied for variations in the suction parameter A, the elastic parameter Λ and the frequency parameter Ω. The effect of the elastic parameter is to decrease the amplitude of skin friction at the upper plate as the suction parameter increases and to decrease the amplitude of the skin friction at the lower plate as the suction parameter decreases.     

MHD Hartmann flow of a dusty fluid with exponential decaying pressure gradient

In the present study, the unsteady Hartmann flow with heat transfer of a viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below while the fluid is acted upon by an external uniform magnetic field applied perpendicular to the plates. The equations of motion are solved analytically to yield the velocity distributions for both the fluid and dust particles. The energy equations for both the fluid and dust particles including the viscous and Joule dissipation terms, are solved numerically using finite differences to get the temperature distributions. On leave from: Department of Engineering Mathematics and physics, Fac. of Engineering, El-Fayoum University, El-Fayoum, Egypt.     

Two-phase non-linear model for the flow through stenosed blood vessels

Pulsatile flow of a two-phase model for blood flow through arterial stenosis is analyzed through a mathematical analysis. The effects of pulsatility, stenosis, peripheral layer and non-Newtonian behavior of blood, assuming the blood in the core region as a Herschel-Bulkley fluid and the plasma in the peripheral layer as a Newtonian fluid, are discussed. A perturbation method is used to solve the resulting system of non-linear quasi-steady differential equations. The expressions for velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. It is noticed that the plug core radius and resistance to flow increase as the stenosis size increases while all other parameters held constant The wall shear stress increases with the increase of yield stress while keeping other parameters as invariables. It is observed that the velocity increases with the axial distance in the stenosed region of the tube upto the maximum projection of the stenosis. Currently on leave from Department of Mathematics, Crescent Engineering College Vandalur, Chennai-600 048, Tamil Nadu, India.     

Two-fluid Herschel-Bulkley model for blood flow in catheterized arteries

The steady flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the core region of suspension of all the erythrocytes as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is observed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases when all the other parameters held constant. It is noticed that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly much smaller for the present two-fluid model than those of the single-fluid model. Presently on leave from Department of Mathematics, B. S. A. Crescent Engineering College, Vandalur, Chennai-48, India)     

The effect of suction and injection on unsteady flow of a dusty conducting fluid in rectangular channel

In the present study, the unsteady Hartmann flow of a dusty viscous incompressible electrically conducting fluid under the influence of an exponentially decreasing pressure gradient is studied without neglecting the ion slip. The parallel plates are assumed to be porous and subjected to a uniform suction from above and injection from below. The fluid is acted upon by an external uniform magnetic field which is applied perpendicular to the plates. An analytical solution for the governing equations of motion is obtained to yield the velocity distributions for both the fluid and dust particles.     

Numerical simulation of fully developed flow and heat transfer characteristics in a curved tube with pulsating pressure gradient

Characteristics of fluid flow and convective heat transfer of a pulsating flow in a curved tube have been investigated numerically. The tube wall is assumed to be maintained at a uniform temperature peripherally in a fully developed pulsating flow region. The temperature and flow distributions over a cross-section of a curved tube with the associated velocity field need to be studied in detail. This problem is of particular interest in the design of Stirling engine heat exchangers and in understanding the blood flow in the aorta. The time-dependent, elliptic governing equations are solved, employing finite volume technique. The periodic steady state results are obtained for various governing dimensionless parameters, such as Womersley number, pulsation amplitude ration, curvature ratio and Reynolds number. The numerical results indicate that the phase difference between the pressure gradient and averaged axial velocity increases gradually up to π/2 as Womersley number increases. However, this phase difference is almost independent of the amplitude ratio of pulsation. It is also found that the secondary flow patterns are strongly affected by the curvature ratio and Reynolds number. These, in turn, give a strong influence on the convective heat transfer from the pipe wall to the pulsating flow. The results obtained lead to a better understanding of the underlying physical process and also provide input that may be used to design the relevant system. The numerical approach is discussed in detail, and the aspects that must be included for an accurate simulation are discussed.     

A numerical study on flow and heat transfer characteristics of film cooling with a compound angle hole

A numerical simulation has been performed for the investigation of flow and heat transfer characteristics of a film cooling system injected through a hole with compound angle orientation. The finite volume method is employed to discretize the governing equations based on the non-orthogonal coordinate with non-staggered variable arrangement. In order to analyze flow and heat transfer characteristics, velocity, temperature, aerodynamic loss coefficient, skin friction and vorticity are calculated with the variation of the skew angle. The maximum longitudinal vorticity and aerodynamics loss depend strongly on the skew angle. For the symmetric case of β=0 deg, a pair of counter-rotating vortices are formed and the maximum value of the film cooling effectiveness has appeared in the center plane where the skin friction is the minimum. For the skew angle of β=30 deg and above, only one strong counter-clockwise vortex remains in the downstream region and the maximum value of the film cooling effectiveness are obtained on the right side of the vortex. The predicted results for the film cooling effectiveness show good agreements with previous experimental data except the near-hole region.     

Three-dimensional MHD simulations of the electromagnetic flowmeter for laminar and turbulent flows

The interaction between an electrically conducting fluid and an external magnetic field in an ideal cylindrical electromagnetic flowmeter is numerically investigated for both laminar and turbulent flows. Induced electric potential in the fluid, and the difference in potential at the measuring electrodes are directly obtained by including MHD effects in the CFD simulations. Fully developed laminar and turbulent flows are simulated. The computed electric potential difference on the electrodes agrees with analytical values for small Hartmann number cases, where the induced Lorentz force is small. Turbulent flow produces a more uniform electric potential distribution in the flow meter cross-section than laminar flow. These integrated MHD/CFD simulations couple the MHD effect with flow dynamics without deriving a weighting function with an assumed velocity profile, which will be necessary for electromagnetic flow meters when the Hartmann number is not small.     

An inclined porous slider bearing with a transverse magnetic field

A hydromagnetic inclined porous slider bearing with a transverse magnetic field is analysed. Expressions for various bearing characteristics are obtained for large and small Hartmann numbers. The dimensionless load capacity, friction and centre of pressure are computed for large Hartmann numbers in the open-circuit case; the load capacity and friction increase markedly with increasing Hartmann number.     

大轴径离心压缩机磁流体密封传热特性研究

高温会降低磁流体饱和磁化强度,造成永磁铁退磁,影响磁流体密封装置的可靠性及稳定性。为探讨磁流体密封装置传热特性,以大轴径离心压缩机磁流体密封为研究对象,同时考虑磁流体摩擦热和轴承摩擦热对磁流体密封装置传热特性的影响,利用有限元数值计算与磁流体、轴承摩擦功耗理论分析相结合的方法,研究磁流体密封装置温度分布规律,分析齿宽、密封间隙和转速对永磁铁和磁流体最高稳态温度的影响,并确定相关工况所需冷却液质量流率。结果表明：由于轴径尺寸较大,表面线速度高,磁流体黏性摩擦热及轴承摩擦热对密封装置传热特性有显著影响,在无冷却工况下,密封装置最高温度超过磁流体和永磁铁的极限使用温度,需通过强制对流换热的方式进行降温处理;永磁铁及磁流体最高稳态温度随着齿宽增加而升高,随着密封间隙增加而减小;随着转速的增加,永磁铁及磁流体最高稳态温度升高,且转速越大,相同转速梯度差之间的温度差越大。     

Three-dimensional features of MHD flows turning in a right-angle duct

This study presents a numerical simulation of three-dimensional (3D) Liquid metal (LM) Magnetohydrodynamic (MHD) flows turning in a right-angle duct with a square cross section under a uniform magnetic field applied perpendicular to the plane of the main flow. The 3D features of the flow in a fluid region adjacent to the duct walls of the turning segment are investigated. Cases with different Hartmann numbers and conductance parameters are analyzed using the CFX code. The MHD features of the LM flow are examined in terms of fluid velocity, current density, electric potential, and pressure gradient. The formation of a velocity recirculation is observed in the inner region of the right-angle segment immediately after the turning of the flow because of the inertial force therein, thereby yielding a region of low electric potential with a complicated current distribution. In particular, in the right-angle segment, the axial velocity in the side layer near the outer wall (that is, in the outer side layer) is relatively lower than that in the inflow and outflow channels. In addition, the velocity recirculation region in the right-angle segment decreases and the pressure gradient increases with an increase in conductance parameter.     

Hall effect on unsteady Hartmann flow with heat transfer under exponential decaying pressure gradient

The unsteady Hartmann flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel non-conducting porous plates is studied with heat transfer taking the Hall effect into consideration. An external uniform magnetic field and a uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to an exponential decaying pressure gradient. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are included in the energy equation. The effect of the ion slip and the uniform suction and injection on both the velocity and temperature distributions is examined. On leave from: Department of Engineering Mathematics and physics, Fac. of Engineering, El-Fayoum University, El-Fayoum, Egypt.     

The frictional behavior of mild steel under horizontal vibration

The present paper investigates experimentally the effect of external horizontal vibration on friction property of mild steel. To do so, a pin-on-disc apparatus having facility of vibrating the test samples in horizontal direction was designed and fabricated. Horizontal vibration is created along the sliding direction of vibration and perpendicular to the direction of vibration. The experimental setup has the facility to vary the amplitudes and frequencies of vibration while velocity of vibration is kept constant. During the experiment, the frequency and amplitude of vibration were varied from 0 to 500 Hz and 0 to 200 μm, respectively. Results show that the friction coefficient increases with the increase in amplitude and frequency of vibration for mild steel. The horizontal vibration can be of two types: one along the direction of sliding (longitudinal direction) and the other along the perpendicular direction of sliding (transverse direction). For both the cases, test sample slides horizontally. It is found that the magnitude of friction coefficient for longitudinal vibration is less than that for under transverse vibration. These results are analyzed by dimensional analysis to correlate the friction coefficient with sliding velocity, frequency and amplitude of vibration. The experimental results are also compared with those available in literature and simple physical explanations are provided.     

Numerical investigation of buoyancy effects on hydromagnetic unsteady flow through a porous channel with suction/injection

The paper focus on first and second laws analysis for flow and heat transfer inside a vertical channel made of two uniformly porous parallel plates with suction/injection under the combined action of buoyancy force, transverse magnetic field and constant pressure gradient. Both vertical walls are kept isothermal at the same temperatures and the flow of the conducting fluid is assumed to be unsteady with variable viscosity. The nonlinear governing equations in Cartesian coordinate are obtained and solved numerically using semi-implicit finite difference techniques to develop expressions for velocity and temperature profiles. The entropy generation number, irreversibility distribution ratio and Bejan number are presented graphically and discussed quantitatively for various values of the embedded parameters.     

The effect of longitudinal tangential vibrations on friction and driving forces in sliding motion

The main purpose of the work has been to qualitatively and quantitatively analyse the influence of longitudinal tangential vibrations on friction and driving forces in a sliding motion. Computational models were developed and implemented in a combined Matlab-Simulink environment. Both the dynamic Dahl's and the Dupont's and classical Coulomb's friction models were used. The influence of vibration velocity amplitude on the friction force in the presence of tangential longitudinal vibrations and on reduction of the driving force in sliding motion was analysed. It revealed that the commonly accepted view that the reduction of the average friction force is a consequence of cyclic changes in the sign of the friction force vector, only when the amplitude of vibration velocity is greater than the sliding motion velocity, is erroneous. The phenomenon was also observed without any changes in the sign of friction force vector. The results of simulations were compared with experimental data obtained with the use of a test rig specifically designed for the work. The Dahl's friction model led to the best correlation.