A numerical model on pulsatile flow of magnetic nanoparticles as drug carrier suspended in Herschel–Bulkley fluid through an arterial stenosis under external magnetic field and body force

ABSTRACT

A theoretical model for blood flow through an artery with stenosis carrying magnetic particles in the presence of magnetic field and periodic body acceleration is analysed. In the present study, blood is assumed to be Herschel–Bulkley fluid carrying iron oxide nanoparticles. The governing equations are highly non-linear and were solved numerically. The effects of model parameters are investigated and the results are represented graphically. The shear stress at the arterial wall and resistive impedance increases with enhancing values of stenotic height, yield stress, flow behaviour index, consistency index, pulsatile Reynolds number, amplitude of body acceleration, particle concentration and particle mass parameters. In order to treat the circulation disorders, control of the parameters involved in blood flow is necessary. The present model is useful in normalizing the parameter values and hence it can be applied in the field of medicine. The study has significant applications in drug delivery for treating cancer.     

Some requirements for electronic properties of a material for MHD: Thermal emission of electrons

There have been significant advances in MHD (magnetohydrodynamics) conversion recently. Hower, the lifetime of electrodes remains too short due to degradation derived from several mechanisms. Electrical degradation is a consequence of an ionic conductivity contribution and of inefficient thermal emission of electrons. The last factor is analyzed for oxides. Point defects are important to understand the effect of the gaseous environment and influence mainly the preexponential term in electron emission expressions. A correlation between the electron affinity and the band gap E _g may help to determine a rough value of . Oxides with low electron affinity and appropriate doping appear attractive for further research.     

3D MHD Jet in a Non-Uniform Magnetic Field

The purpose of this paper is to present a two-phase 3D magnetohydrodynamics （MHD） flow model that combines the volume of fluid （VOF） method with the technique derived from induced-magnetic-field equations for liquid metal free surface MHD-jet-flow. Analogy between the induced-magnetic-filed equation and the conventional computational fluid dynamics （CFD） equation is made, so that the equation can be conveniently accounted for by CFD. A penalty factor numerical method is introduced in order to force the local divergence-free condition of the magnetic fields and an extension of the void insulating calculation domain is applied to ensure that the induced-magnetic field at its boundaries is null. These simulation results for lithium liquid metal jets under magnetic field configurations of Magnetic Torus （Mtor） and National Spherical Torus Experiment （NSTX） outboard divertor have shown that three dimensional jet can not be annihilated by magnetic braking and its cross-section will deform in such a way that the momentum flux of the jet is conserved. 3D MHD effects from a magnetic field gradient cause return currents to interact with applied magnetic fields and produce unfavorable Lorentz forces. Under 3D applied non-uniform magnetic fields of the divertor, unfavorable Lorentz forces lead to a substantial change in flow pattern and a reduction in flow velocity, with the jet cross-section moving to one side of the jet space. These critical phenomena can not be revealed by 2D models.     

对二维磁流体翼升力原理的几点讨论

本文讨论了磁流体翼的数学基础,即二维机翼理论在磁流体翼中适用的条件。本文得到了要使二维机翼理论成立电磁场所要满足的必要条件。为了讨论这一设想的有效性,本文引入了零攻角平板磁流体绕流的物理模型和数值计算的数学模型,并给出了相关的结果以及磁流体翼的一些基本的物理性质。     

Nonlinear magnetohydrodynamic flow of nanofluids across a porous matrix over an extending sheet with mass transpiration and bioconvection

The consequences of the nonlinear magnetic field and radiative thermal energy are evaluated for bioconvective viscous flow across a porous matrix over a nonlinearly stretching sheet. The rationale of the study is to attain enhanced thermal transportation. The dilute dispersion of nanoentities and bioconvection of swimming microorganisms are taken into consideration. The coupled partial differential system of field equations is transformed into ordinary differential form. Finally, the numeric solution is obtained by utilizing the fourth-order Runge–Kutta method shooting technique, and results are validated through an acceptable accord with existing studies. The variation of influential parameters such as combined magnetic parameter, mass transpiration parameter, thermophoresis, Brownian motion, bioconvection Lewis numbers made notable impacts on fluid velocity, temperature, concentration of nanoentities, and distribution of microorganisms.     

Activation energy and binary chemical reaction on unsteady MHD Williamson nanofluid containing motile gyrotactic micro‐organisms

The author presents the influence of Arrhenius activation energy and binary chemical reaction on an unsteady magnetohydrodynamics Williamson nanofluid with motile gyrotactic micro‐organisms. The governing equations are converted to coupled ordinary differential equations with similarity transformations and the fifth‐order Runge‐Kutta Fehlberg method and the shooting algorithm is applied to solve these equations using the appropriate boundary conditions. A detailed investigation considering the effects of different physical parameters on the profiles like velocity, temperature, concentration, and density of motile gyrotactic micro‐organisms was done and plotted graphically. It is found that the thermal boundary layer enhances for the chemical reaction rate and the solutal boundary layer increases for activation energy. Furthermore, the nondimensional Williamson parameter reduces for the velocity profile. The author studied the wall temperature gradient of different fluids and found that temperature gradient decreased for the present study. Comparisons of the present result with published work were done to verify the present code.     

Nonlinear Boussinesq buoyancy driven flow and radiative heat transport of magnetohybrid nanoliquid in an annulus: A statistical framework

The effect of nonlinear Boussinesq buoyancy force on the flow of Cu-Al₂O₃-H₂O hybrid nanoliquid in a vertical annulus, which is adjacent to the radial magnetic field and thermal radiation, is analyzed through a statistical approach. The phenomena of movement of annuli are taken into account. The aspect of nonlinear density temperature is also accounted based on nonlinear Boussinesq approximation (NBA). The exact solution is obtained for the two-point boundary value problem comprised dimensionless governing equations. The skin friction coefficient and Nusselt number expressions are also estimated. The impacts of various physical parameters on the velocity, temperature, skin friction coefficient, and Nusselt number distributions are analyzed. The statistical techniques, such as correlation coefficient, probable error, and a multivariate regression model, are employed for the detailed analysis. It is found that the NBA is favorable for the skin friction coefficient and the rate of heat transfer. The maximum heat transfer is found on the wall of the internal annuli.     

Finite element analysis of non‐Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery

The present study considers two‐dimensional mathematical modeling of non‐Newtonian nanofluid hemodynamics with heat and mass transfer in a stenosed coronary artery in the presence of a radial magnetic field. The second‐grade differential viscoelastic constitutive model is adopted for blood to mimic non‐Newtonian characteristics, and blood is considered to contain a homogenous suspension of nanoparticles. The Vogel model is employed to simulate the variation of blood viscosity as a function of temperature. The governing equations are an extension of the Navier‐Stokes equations with linear Boussinesq's approximation and Buongiorno's nanoscale model (which simulates both heat and mass transfer). The conservation equations are normalized by employing appropriate nondimensional variables. It is assumed that the maximum height of the stenosis is small in comparison with the radius of the artery, and, furthermore, that the radius of the artery and length of the stenotic region are of comparable magnitude. To study the influence of vessel geometry on blood flow and nanoparticle transport, variation in the design and size of the stenosis is considered in the domain. The transformed equations are solved numerically by means of the finite element method based on the variational approach and simulated using the FreeFEM++ code. A detailed grid‐independence study is included. Blood flow, heat, and mass transfer characteristics are examined for the effects of selected geometric, nanoscale, rheological, viscosity, and magnetic parameters, that is, stenotic diameter (d), viscoelastic parameter (), thermophoresis parameter (), Brownian motion parameter (), and magnetic body force parameter (M) at the throat of the stenosis and throughout the arterial domain. The velocity, temperature, and nanoparticle concentration fields are also visualized through instantaneous patterns of contours. An increase in magnetic and thermophoresis parameters is found to enhance the temperature, nanoparticle concentration, and skin‐friction coefficient. Increasing Brownian motion parameter is observed to accelerate the blood flow. Narrower stenosis significantly alters the temperature and nanoparticle distributions and magnitudes. The novelty of the study relates to the combination of geometric complexity, multiphysical nanoscale, and thermomagnetic behavior, and also the simultaneous presence of biorheological behavior (all of which arise in actual cardiovascular heat transfer phenomena) in a single work with extensive visualization of the flow, heat, and mass transfer characteristics. The simulations are relevant to the diffusion of nano‐drugs in magnet‐targeted treatment of stenosed arterial disease.     

MHD dissipative fluid past a stretching sheet in the presence of Soret effect with Newtonian convective heat and mass conditions

This article deliberates a theoretical study on a two‐dimensional magnetohydrodynamic free convection flow of an electrically conducting, heat generation/absorption fluid flowing past a linearly stretching sheet, placed vertical in a non‐Darcian porous medium with Soret effect. As the magnetic Reynolds number of the flow field considered very small (due to noncomparability of the induced and applied magnetic fields), the influence of the induced magnetic field is thus neglected. Again due to weak applied voltage differences at the lateral ends, the influence of the electric current is also ignored. A homotopy analysis method is developed to solve the similarity transformed equations subject to a set of convective heat and mass boundary conditions. Numerical data simulations are made on various fluid variables by using some practical/selected values of the governed parameters and illustrated through graphs and tables. It is found that the Newtonian heating parameter enhanced the velocity, temperature, and concentrations, while the solutal Newtonian heating parameter accelerates the rate of flow of heat and masses but minimizes the temperature gradient. The local Forchheimer and dissipation parameters are found to raise the temperature and concentrations, while the flow rate accelerates due to dissipation parameter but decelerates in presence of Forchheimer parameter.