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The purpose of this paper is to model the particle capture of elliptic magnetic matrices for parallel stream type high magnetic separation, which can be a guidance for the development of novel elliptic cylinder matrices for high-gradient magnetic separation (HGMS).

The magnetic field distribution around the elliptic matrices is investigated quantitatively and the magnetic field and gradient were calculated. The motion equations of the magnetic particles around the matrices were derived and the particle capture cross-section of elliptic matrices was studied and was compared with that of the conventional circular matrices.

Elliptic matrices can present larger particle capture cross-section than the conventional circular matrices and can be a kind of promising matrices to be applied to HGMS.

There is little literature investigating the magnetic characteristics and the particle capture of the elliptic matrices in HGMS, the study is of great significance for the development of novel elliptic magnetic matrices in HGMS.

The purpose of this paper is used to study the combined effect of solute gradient and magnetic field on dusty couple-stress fluid in the presence of rotation through a porous medium.

The perturbation technique (experimental method) is applied in this study.

For the case of stationary convection, solute gradient and rotation have stabilizing effect, whereas destabilizing effect is found in dust particles in the system. Couple stress and medium permeability both have dual character to its stabilizing effect in the absence of magnetic field and rotation. Magnetic field succeeded in establishing a stabilizing effect in the absence of rotation.

The results are discussed by allowing one variable to vary and keeping other variables constant, as well as by drawing graphs.

This study aims to investigate thermo-bioconvection of oxytactic microorganisms occurring in a nanofluid-saturated porous lid-driven cavity in the presence of the magnetic field. The heating is provided through a bell-shaped curved bottom wall heated isothermally. The effects of the peak height of the curved bottom wall, bioconvection Rayleigh number (Rb), Darcy number (Da), Hartmann number (Ha), Peclet number (Pe), Lewis number (Le) and Grashof number (Gr) on the flow structure, temperature and the iso-concentrations of oxygen and microorganisms are examined and explained systematically. The local and global, characteristics of heat transfer and oxygen concentration, are estimated through the Nusselt number (Nu) and Sherwood number (Sh), respectively.

The governing equations of continuity, momentum, energy and additionally consisting of species transport equations for oxygen concentration and population density of microorganisms, are discretized by the finite volume method. The evolved linearized algebraic equations are solved iteratively through the alternate direction implicit scheme and the tri-diagonal matrix algorithm. The computation domain has meshed in non-uniform staggered grids. The entire computations are carried out through an in-house developed code written in FORTRAN following the SIMPLE algorithm. The third-order upwind and second-order central difference schemes are used for handling the advection and diffusion terms, respectively. The convergence criterion for the iterative process of achieving the final solution is set as 10–8 and 10–10, respectively, for the maximum residuals and the mass defect.

The results show that the flow and temperature distribution along with the iso-concentrations of oxygen and microorganisms are markedly affected by the curvature of the bottom wall. A secondary circulation is developed in the cavity that changes the flow physics significantly. The Nu increases with the peak height of the curved bottom wall and Da; however, it decreases with Ha and Rb. The Sh increases with Da but decreases with Ha and the peak height of the curved wall.

A similar study of bioconvection could be extended further considering thermal radiation, chemical attraction, gravity, light, etc.

The outcomes of this investigation could be used in diverse fields of multi-physical applications such as in food industries, chemical processing equipment, fuel cell technology and enhanced oil recovery.

The insights of bioconvection of oxytactic microorganisms using a curved bottom surface along with other physical issues such as nanofluid, porous substance and magnetic field are addressed systematically and thoroughly.

The objective of present research is to characterize the unsteady thermal behavior of a square enclosure filled with water-Al₂O₃ nanofluids in the presence of oriented magnetic fields. The purpose this paper is to study the effect of pertinent parameters on the transient natural convection in the enclosure.

In this research, an in-house implicit finite volume code based on the SIMPLE algorithm is utilized for numerical calculations. To ensure the accuracy of results, comparisons are also made with previous works in literature. In this study, a constant strength magnetic field is concerned and for Rayleigh numbers of Ra=103, 104 and 105 the effect of magnetic field orientation with respect to the case of zero inclination on the thermal performance of cavity is investigated at Hartmann number range of Ha=15-90. In the present work, the nano-particle volume fractions range from φ=0-0.06.

Results show that when Rayleigh number is Ra=103, the inclination angle, solid particles and Hartmann number has no effect on the transient behavior. It is shown that during the time advancement to steady condition, the heat transfer rate relative to zero inclination angle, may reach to a maximum value. This relative maximum heat transfer increases as the inclination angle increases and decreases as the solid volume fraction increases. The effect of increase in Hartmann number is to decrease this maximum value at Rayleigh number of Ra=104 and at Rayleigh number of Ra=105, depending on the Hartmann number, this value may increase or decrease. It is also found that an increase in Hartmann number leads to delay the appearance of the relative maximum value of heat transfer. Results show that this maximum value is of more significance at zero solid volume fraction when inclination angle is 90 degrees and Hartmann number is Ha=60.

Limited works could be found in the literature regarding the idea of using nanofluids as the working fluid in an enclosure in the presence of magnetic field. In these works, the steady state thermal behavior of enclosures subjected to fixed magnetic fields is concerned. In the present work, the unsteady thermal behavior is concerned and the effect of magnetic field orientation angles on transient heat transfer performance of the enclosure at different Rayleigh and Hartmann numbers and solid volume fractions is explored.

The purpose of this paper is to study the unsteady ferrofluid flow with a hot source helix inside a cavity under the impacts of a variable magnetic field by using the incompressible smoothed particle hydrodynamics method.

The governing equations are formulated by considering the basics of the magnetohydrodynamic and ferrohydrodynamics. Different locations of a variable magnetic source outside the geometry are investigated. The helical coils are extensively applied in the cooling and heating of air conditioners and heat pumps. Computations were carried out for different lengths of the heated helix (0.2 ≤ L_h ≤ 0.8), different locations of the magnetic source, (a = 0.5, b = −0.01), (a = 0.5, b = 1.01), (a = 1.01, b = 0.5), (a = −0.01, b = 0.5), different numbers of the inner helix (one helix, two helixes and three helixes) and different values of the nanoparticles volume fraction (0% ≤ ϕ ≤ 10%).

The outcomes of the investigations revealed that an increase in the lengths of a helix by 0.4 results in a reduction of the stream function by 25.60%. In addition, when the magnetic wire is located near the center of the right wall, the maximum values of the average Nusselt number are obtained while the smallest values of the average Nusselt number are given when the magnetic source is located near center of the top wall.

The novelty of this paper is investigating the natural convection flow from two different models of an inner hot helix inside a cavity with considering different locations of variable magnetic sources.

The purpose of this paper is to present novel analytical expressions which describe the 3D magnetic field of arbitrarily magnetized triangular‐shaped charged surfaces. These versatile expressions model that the field of triangular‐shaped permanent magnets (PMs) are very suitable to model skewed slotless machines.

The analytical 3D surface charge method is normally used to provide field expressions for PMs in free space. In this paper, the analytical surface charge integrals are analytically solved for charged right‐triangular surfaces. The resulting field is compared with that obtained by finite element modeling (FEM) and subsequently applied in two examples.

The comparison with FEM shows that the 3D analytical expressions are very accurate and exhibit very low‐numerical noise. These fast‐solving versatile expressions are therefore considered suitable to model triangular‐shaped or polyhedral‐shaped PMs.

The surface charge method assumes that the relative permeability is equal to 1 and therefore soft‐magnetic materials need to be modeled using the method of images. The PMs are assumed to be ideal in terms of homogeneity, magnetization vector, permeability, demagnetization, and geometrical tolerances.

Many applications, such as the subclass of slotless synchronous linear actuators with a skewed PM structure and planar magnetic bearings, are very suitable to incorporate this modeling technique, since it enables the analysis of a variety of performance data.

As an addition to the common 3D analytical field expressions for cuboidal or cylindrical PMs, this paper presents novel expressions for magnets having triangular surfaces.

The fast and flexible development of fast switching electromagnetic valves as used in modern gasoline engine demands the availability of efficient and accurate simulation tools. The purpose of this paper is to provide an enhanced computational scheme of these actuators including all relevant physical effects of magneto‐mechanical systems and including contact mechanics.

The finite element (FE) method is applied to efficiently solve the arising coupled system of partial differential equations describing magneto‐mechanical systems. The algorithm for contact mechanics is based on the cross‐constraint method using an energy‐ and momentum‐conserving time‐discretisation scheme. Although solving separately for the electromagnetic and mechanical system, a strong coupling is ensured within each time step by an iterative process with stopping criterion.

The numerical simulations of the full switching cycle of an electromagnetic direct injection valve, including the bouncing during the closing state, are just feasible with an enhanced and robust mechanical contact algorithm. Furthermore, the solution of the nonlinear electromagnetic and mechanical equations needs a Newton scheme with a line search scheme for the relaxation of the step size.

The paper provides a numerical simulation scheme based on the FE method, which includes all relevant physical effects in magneto‐mechanical systems, and which is robust even for long‐term contact periods with multitude re‐opening phases.

The purpose of this paper is to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third grade fluid in a channel. The principal question the authors address in this paper is in regard to the applicability of the no‐slip condition at a solid‐liquid boundary. The authors present the effects of slip, magnetohydrodynamics (MHD) and heat transfer for the plane Couette, plane Poiseuille and plane Couette‐Poiseuille flows in a homogeneous and thermodynamically compatible third grade fluid. The problem of a non‐Newtonian plane Couette flow, fully developed plane Poiseuille flow and Couette‐Poiseuille flow are investigated.

The present investigation is an attempt to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third grade fluid in a channel. A very effective and higher order numerical scheme is used to solve the resulting system of nonlinear differential equations with nonlinear boundary conditions. Numerical solutions are obtained by solving nonlinear ordinary differential equations using Chebyshev spectral method.

Due to the nonlinear and highly complicated nature of the governing equations and boundary conditions, finding an analytical or numerical solution is not easy. The authors obtained numerical solutions of the coupled nonlinear ordinary differential equations with nonlinear boundary conditions using higher order Chebyshev spectral collocation method. Spectral methods are proven to offer a superior intrinsic accuracy for derivative calculations.

To the best of the authors' knowledge, no such analysis is available in the literature which can describe the heat transfer, MHD and slip effects simultaneously on the flows of the non‐Newtonian fluids.

The purpose of this paper is to investigate the unsteady magnetohydrodynamic (MHD) Couette flow of an electrically conducting incompressible non-Newtonian third grade reactive fluid with temperature-dependent variable viscosity and thermal conductivity properties under isothermal surface conditions.

The coupled non-linear partial differential equations for momentum and energy balance governing the transient problem are obtained and tackled numerically using a semi-discretization finite difference technique.

The effects of various embedded thermophysical parameters on the velocity and temperature fields including skin friction, Nusselt number and thermal stability conditions are presented graphically and discussed quantitatively.

The approach is applicable to modelling the complex physical phenomenon in MHD lubrications that occurs in numerous areas of engineering and industrial processes.

This paper may be of industrial and engineering interest especially in understanding the combined effects of unsteadiness, variable thermophysical properties and magnetic field on the thermal stability condition for a reactive non-Newtonian third grade fluid under Couette flow scenario.

This paper aims to investigate the effect of Powell–Eyring fluid induced by a stretched sheet. Heat and mass transfer under the influence of magnetic dipole over a stretching sheet are taken into account.

Nonlinear coupled governing equations are solved using the optimal homotopy asymptotic technique, and a computer software package BVPh 2.0 is used for numerical computations.

Impact of significant quantities is graphically examined. It is seen that the heat transfer deceases for higher values of viscous dissipation parameter, radiation parameter, Dufour number, whereas it increases for bigger values of Prandtl number. The numerical results have been validated through comparison with existing literature as a special case of proposed model and perceived that the Soret number has reining role to increase the rate of heat transfer.

To the best of the authors’ knowledge, this study is reported for the first time.