Turbulent biomagnetic fluid flow in a rectangular channel under the action of a localized magnetic field

The fundamental problem of the turbulent flow of a biomagnetic fluid (blood) between two parallel plates under the action of a localized magnetic field is studied. The blood is considered to be an electrically conducting, incompressible and Newtonian fluid and its flow is steady, two-dimensional and turbulent. The turbulent flow is described by the Reynolds averaged Navier–Stokes (RANS) equations. For the numerical solution of the problem under consideration, which is described by a coupled and non-linear system of PDEs, with appropriate boundary conditions, the stream function–vorticity formulation is used. For the eddy-kinematic viscosity, the low Reynolds number k–ε turbulence model is adopted. The solution of the problem, for different values of the dimensionless parameter entering into it, is obtained by developing and applying an efficient numerical technique based on finite differences scheme. Results concerning the velocity and temperature field, skin friction and rate of heat transfer, indicate that the presence of the localized magnetic field, appreciable influences the turbulent flow field. A comparison is also made with the corresponding laminar flow, indicating that the influence of the magnetic field decreases in the presence of turbulence.     

The flow of conducting fluids through circular pipes having finite conductivity and finite thickness under uniform transverse magnetic fields

The steady flow of viscous, incompressible, electrically conducting fluids through circular pipes in the presence of an applied uniform transverse magnetic field is considered. In this analysis, the finite conductivity and wall thickness of the pipe have been taken into account. An exact solution and its numerical calculation have been presented. Some interesting results have been obtained.     

Effect of contact resistance on steady MHD flows through circular pipes having constant conductivity and finite wall thickness

The steady flow of viscous, electrically conducting liquids through circular pipes having finite wall thickness and conductivity under an applied uniform transverse magnetic field is considered. A uniform contact resistance at the solid/liquid interface is taken into account. An exact solution and its numerical calculations are presented.     

Magnetorheological rotational flow with viscous dissipation

Effects of a magnetic field and fluid nonlinearity are investigated for the rotational flow of the Carreau-type fluid while viscous dissipation is taken into account. The governing motion and energy balance equations are coupled, adding complexity to the already highly correlated set of differential equations. The numerical solution is obtained for the narrow-gap limit and steady-state base flow. Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow was investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effects of the Hartmann number, the Brinkman number, and the Deborah number on the stability of the flow were investigated. The introduction of the magnetic field induces a resistive force acting in the opposite direction of the flow, thus causing its deceleration. Moreover, the study shows that the presence of magnetic field tends to slow down the fluid motion. It, however, increases the fluid temperature. Moreover, the total entropy generation number decreases as the Hartmann number and fluid elasticity increase and increases with increasing Brinkman number.     

Immersed stress method for fluid–structure interaction using anisotropic mesh adaptation

This paper presents advancements toward a monolithic solution procedure and anisotropic mesh adaptation for the numerical solution of fluid–structure interaction with complex geometry. First, a new stabilized three‐field stress, velocity, and pressure finite element formulation is presented for modeling the interaction between the fluid (laminar or turbulent) and the rigid body. The presence of the structure will be taken into account by means of an extra stress in the Navier–Stokes equations. The system is solved using a finite element variational multiscale method. We combine this method with anisotropic mesh adaptation to ensure an accurate capturing of the discontinuities at the fluid–solid interface. We assess the behavior and accuracy of the proposed formulation in the simulation of 2D and 3D time‐dependent numerical examples such as the flow past a circular cylinder and turbulent flows behind an immersed helicopter in a forward flight. Copyright © 2013 John Wiley & Sons, Ltd.     

Advanced model of laminated magnetic cores for two-dimensionalfield analysis

A numerical model for the analysis of laminated ferromagnetic cores of electromechanical devices is presented. The model is based on the finite-element solution of the two-dimensional (2-D) electromagnetic field problem in the lamination plane; a dynamical relation between local magnetic flux density and magnetic field strength is obtained by solving for the one-dimensional (1-D) eddy-current field developed in the lamination depth. The hysteresis of the magnetic material is accounted for by the Preisach approach. The model is first validated by comparison with an alternative held formulation available for axis-symmetric structures; finally, an application to a more complex 2-D laminated core is presented and the numerical results are confirmed by comparison with measured waveforms of electrical and magnetic quantities     

Unsteady MHD-boundary-layer of a source and vortex flow adjacent to a stationary surface

Summary The steady laminar incompressible flow of an electrically conducting fluid over an infinite permeable disk in the presence of an axial magnetic field has been investigated, and a self-similar solution of the boundary-layer equations is obtained numerically. For large values of the suction parameter, a closed form solution is obtained. Also, an asymptotic solution is found for large values of the independent variable. The surface-shear stresses in the radial and tangential directions and the surface heat transfer strongly depend on the suction parameter, the ratio of the source and vortex flow and the magnetic field except the surface heat transfer which weakly depends on the magnetic field. The similarity solution of the boundary-layer equations exists only when a certain minimum suction or magnetic field is applied. The results of the analytical solution are in good agreement with those of the numerical solution for the suction parameterf _w3.     

Effect of a non-constant magnetic field on natural convection in a horizontal porous layer heated from the bottom

An analytical and numerical investigation is conducted to study the effect of an electromagnetic field on natural convection in a horizontal shallow porous cavity filled with an electrically conducting fluid. The magnetic field is assumed to be induced by two long wires, carrying current, parallel to the horizontal boundaries of the system. A uniform heat flux is applied to the horizontal walls of the layer while the vertical walls are adiabatic. The governing parameters of the problem under study are the thermal Rayleigh number, Ra, Hartmann number, Ha, position of the electrical wires, d, current intensity ratio, r, and aspect ratio of cavity, A. An analytical solution, valid for a shallow layer (A ? 1), is derived on the basis of the parallel flow approximation. The critical Rayleigh number, Ra _c , for the onset of motion is derived in closed form in terms of the parameters of the problem. For finite-amplitude convection the heat and flow characteristics predicted by the analytical model are found to agree well with a numerical study of the full governing equations.     

Non-equilibrium linearized magnetogasdynamic flow over a wavy wall (aligned)

Summary A steady, linearized flow of a conducting fluid withn non-equilibrium processes in parallel has been considered and neglecting the effects due to viscosity, heat conduction and diffusion and assuming the electrical conductivity to be infinite, a single equation for the flow variables has been derived when the undisturbed uniform magnetic field is aligned to the undisturbed uniform fluid stream. The solution of the equation has been obtained for a flow over a two-dimensional wavy wall. The pressure, net pressure i.e. the difference between the local static, pressure and force per unit area arising from the surface current, drag coefficient and total drag coefficient have been calculated and the results have been discussed. It is found that for certain values of the equilibrium Mach number and the magnetic pressure number negative drag coefficient as well as negative total drag coefficient occur in the flow.With 6 Figures     

Hall effects on magnetohydrodynamic free convection about a semi-infinite vertical flat plate

A theoretical analysis is presented for the problem of free convection flow of a conducting fluid along a semi-infinite vertical flat plate when the fluid is permeated by a transverse magnetic field and the Hall effects are taken into account. The derived fundamental equations on the assumption of small magnetic Reynolds number are solved numerically by employing the difference-differential method in combination with the Simpson's rule. The velocity and temperature profiles as well as the local Nusselt number are computed for various values of the Hall and magnetic parameters. The results are compared with those known from the literature.     

Pseudospectral method for MHD pipe flow

The paper deals with MHD flow in pipes with arbitrary wall conductivity under the influence of a transverse magnetic field. We employ the pseudospectral collocation method for obtaining a numerical solution of the problem. The numerical results are compared with analytical ones in the case of pipe with insulating walls. We notice that the magnetic field is slowing the motion. Copyright © 2006 John Wiley & Sons, Ltd.     

BEM modeling of saturated porous media susceptible to damage

This paper deals with the numerical analysis of saturated porous media, taking into account the damage phenomena on the solid skeleton. The porous media is taken into poro-elastic framework, in full-saturated condition, based on Biot’s Theory. A scalar damage model is assumed for this analysis. An implicit boundary element method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and two-dimensional elastostatic problems. The integration over boundary elements is evaluated using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear problem is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficacy.     

Motion of paramagnetic particles in a viscous fluid under a uniform magnetic field: benchmark solutions

Numerical simulations of the two-dimensional motion of multiple paramagnetic particles suspended in a viscous fluid subjected to a uniform magnetic field are presented. Both the magnetic field and flow field can be described efficiently with simple series in local coordinates attached to each particle. The coefficients of the series can be obtained with fast convergence when only a few leading coefficients are treated implicitly. Numerical results for the flow field are validated by comparing the data with those given by an asymptotic solution for a pair of particles separated by a small distance. The numerical results of the magnetic field are validated by comparison with the solutions in bipolar coordinates. Simulations of the motion of multiple particles reveal interesting phenomena and shed light on the fundamental mechanism of particles clustering into a straight chain. The data presented in this paper can be used as a benchmark solution for verifying codes for simulating the motion of paramagnetic particles in a magnetic field.     

Asymptotic analysis and finite element calculation of a rubber cone under tension

Summary The problem of a cone under tension of a concentrated load at its tip is investigated by adopting the constitutive equation of rubber-like materials given by Knowles and Sternberg (1973). The problem was treated as axial-symmetry case, and large deformation was taken into account. The asymptotic solution to the stress-strain field near the apex of the cone is obtained and solved analytically. By means of the finite element method, the stress-strain field is also calculated. The numerical results are consistent well with that of the analysis.     

A FAST NUMERICAL METHOD FOR ISOTHERMAL RESIN TRANSFER MOLD FILLING

An efficient numerical scheme is presented for simulating isothermal flow in resin transfer molding. The problem involves transient, free surface flow of an incompressible fluid into a non-deforming porous medium. A new variant of the Control Volume Finite Element (CVFE) algorithm is explained in detail. It is shown how the pressure solutions at each time step can be obtained by adding a single row and column to the Cholesky factorization of the stiffness matrix derived from a finite element formulation for the pressure field. This approach reduces the computation of a new pressure solution at each time step to essentially just two sparse matrix back-substitutions. The resulting performance improvement facilitates interactive simulation and the solution of inverse problems which require many simulations of the filling problem. The computational complexity of the calculation is bounded by O(n^2⋅5), where n is the number of nodes in the finite element mesh. A 100-fold speedup over a conventional CVFE implementation was obtained for a 2213-node problem.     

Integral formulation to simulate the viscous sintering of a two-dimensional lattice of periodic unit cells

In this paper a mathematical formulation is presented which is used to calculate the flow field of a two-dimensional Stokes fluid that is represented by a lattice of unit cells with pores inside. The formulation is described in terms of an integral equation based on Lorentz's formulation, whereby the fundamental solution is used that represents the flow due to a periodic lattice of point forces. The derived integral equation is applied to model the viscous sintering phenomenon, viz. the process that occurs (for example) during the densification of a porous glass heated to such a high temperature that it becomes a viscous fluid. The numerical simulation is carried out by solving the governing Stokes flow equations for a fixed domain through a Boundary Element Method (BEM). The resulting velocity field then determines an approximate geometry at a next time point which is obtained by an implicit integration method. From this formulation quite a few theoretical insights can be obtained of the viscous sintering process with respect to both pore size and pore distribution of the porous glass. In particular, this model is able to examine the consequences of microstructure on the evolution of pore-size distribution, as will be demonstrated for several example problems.     

Three-dimensional flow with heat transfer of a viscoelastic fluid over a stretching surface with a magnetic field

The present research study deals with the steady flow and heat transfer of a viscoelastic fluid over a stretching surface in two lateral directions with a magnetic field applied normal to the surface. The fluid far away from the surface is ambient and the motion in the flow field is caused by stretching surface in two directions. This result is a three-dimensional flow instead of two-dimensional as considered by many authors. Self-similar solutions are obtained numerically. For some particular cases, closed form analytical solutions are also obtained. The numerical calculations show that the skin friction coefficients in x- and y-directions and the heat transfer coefficient decrease with the increasing elastic parameter, but they increase with the stretching parameter. The heat transfer coefficient for the constant heat flux case is higher than that of the constant wall temperature case.     

ON A NUMERICAL METHOD FOR THE EVALUATION OF ELECTROMAGNETIC LOSSES IN ELECTRIC MACHINERY

The paper deals with a numerical method for the evaluation of the magnetic iron losses in steel laminations used in rotating electric machinery. The magnetic hysteresis and the eddy current effects are directly and simultaneously taken into account. Hereby commonly used analytic expressions for the distribution function in the widely adapted Preisach hysteresis model are found to be not quite accurate. The magnetic circuit is decomposed into magnetic and air gap network elements, connected by fundamental loops. The magnetic network elements show a finite element structure. The kinematics of the electric machine is deliberately taken into account by an interpolation technique. Although the model retains the essential features of a cumbersome 3-D problem, a relatively simple algorithm may be developed. For the resulting algebraic system, we propose a suitable decoupling technique, which is efficient from the computational point of view. Numerical experiments show that the results obtained by our numerical approach are in good agreement with the known behaviour of the magnetic material.     

Localized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions

In this article a numerical solution of the time dependent, coupled system equations of magnetohydrodynamics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approximation of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collocation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform magnetic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for several Hartmann numbers (up to 10⁵) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form meshless methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local Petrov–Galerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L ₂ and L _∞, the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems.     

Numerical analysis of high-frequency induction heating includingtemperature dependence of material characteristics

We have carried out a numerical analysis of the magnetic field on high-frequency induction heating. This analysis includes the dependence of various magnetic properties on temperature. The required characteristics are obtained experimentally. We compare the experimental results with the theoretical values obtained by approximations. Until now, the current density inside the exciting coil on this kind of problem has been assumed to be uniform, which is different from actual phenomena. We propose a new method which takes the inhomogeneous distribution of exciting current into account. In this analysis, the eddy current of the exciting coil is also taken into account