非牛顿磁性纳米流体旋转流动

研究非牛顿磁性纳米磁体定常旋转流动。考虑到磁化强度的特殊贡献,应用修正的非牛顿磁性流体运动方程,磁场作用是纯扩散,不受流体运动速度场的影响。给出了多种流动的解析解。应用计算机符号运算技术,软件Maple16,可以得岀非牛顿上随体Maxwell磁性纳米流体和Oldroyd B磁性纳米流体非定常流动方程的各级近似解的常微分方程,获得解析和数值解。在研究中对纳米流体的物质常数作纳米修正。     

回归分析法在舰船周围空间固定磁场建模中的应用

近年来 ,我们在舰船周围空间固定磁场的建模方面做了大量工作 ,取得了一些进展 ,为进一步实现对舰船固定磁性的实时监控打下了良好的基础 .本文对基于多元线性回归分析方法的舰船周围空间固定磁性线形模型的建立及其仿真结果进行介绍     

磁流变弹性体的力-磁耦合模型

以磁偶极子理论为基础,利用最小势能原理,从微观角度出发,研究了磁流变弹性体在单向载荷作用下的力-磁耦合行为,提出了可以描述该行为的数学模型,分析了磁致应力非线性变化的规律和机理.该模型从磁流变弹性体的微观结构出发,考虑了所有铁磁颗粒的磁化特性,以及颗粒之间、链结构之间的相互作用,推导了磁相互作用能的表达式,采用Mooney-Rivlin模型给出了弹性势能表达式.最后运用最小势能原理,建立了描述磁流变弹性体在均匀磁场中力-磁耦合行为的数学模型.该模型与实验结果吻合较好,并能从微观层面对磁流变弹性体的磁致应力变化规律做出解释.研究发现,磁流变弹性体的磁致应力在不同磁场下的变化规律不同,与材料内部的微结构紧密相关,铁磁颗粒之间及链结构之间的相互作用是导致磁致应力非线性变化的主要原因.     

流经有热源多孔平板并伴有化学反应的传热传质混合对流MHD流动

对流经无限竖直多孔平板的不可压缩粘性导电流体,稳定的传热传质混合对流MHD流动问题,给出了精确解和数值解.假定均匀磁场横向作用于流动方向,考虑了感应磁场及其能量的粘性和磁性损耗.多孔平板有恒定的吸入速度并均匀地混入流动速度.用摄动技术和数值方法求解控制方程.得到了平板上速度场、温度场、感应磁场、表面摩擦力和传热率的分析表达式.相关参数取不同数值时,用图形表示出问题的数值结果.讨论了从平板到流体的Hartmann数、化学反应参数、磁场的Prandtl数,以及包括速度场、温度场、浓度场和感应磁场等其它参数的影响.可以发现,热源/汇或Eckert数的增大,极大地提高了流体的速度值.x-方向的感应磁场随着Hartmann数、磁场的Prandtl数、热源/汇和粘性耗散的增大而增大.但是,研究表明,随着破坏性化学反应(K0)的增大,流动速度、流体温度和感应磁场将减小.对色谱分析系统和材料加工的磁场控制,该研究在热离子反应堆模型、电磁感应、磁流体动力学传输现象中得到了应用.     

伴有磁场和纳米固体颗粒时的Jeffery-Hamel流动解析研究——Adomian分解法

用一种强有力的解析方法,称为Adomian分解法(ADM),来研究磁场和纳米颗粒对Jeffery-Hamel流动的影响.将该问题模型的控制方程,即将传统的流体力学Navier-Stokes方程和Maxwell电磁方程,简化为非线性的常微分方程.该方法得到的结果与Runge-Kutta方法得到的数值结果相一致,结果用表格列出.不同α,Ha和Re数下的图形表明,本方法可以得到高精度的结果.首先对不同的Hartmann数和管壁倾角,研究喇叭形管道中的流场;最后在没有磁场作用时,研究纳米固体颗粒体积率的影响.     

磁弹性耦合效应引起的铁磁直杆磁场中振动频率的改变

基于磁弹性广义变分原理和Hamilton原理,对处于外加磁场中的软铁磁体,建立了磁弹性动力学理论模型．分别通过关于铁磁杆磁标势和弹性位移的变分运算,获得了包含磁场和弹性变形的所有基本方程,并给出描述磁弹性耦合作用的磁体力和磁面力．采用摄动技术和Galerkin方法,将所建立的磁弹性理论模型用于外加磁场中铁磁直杆的振动分析．结果表明,由于磁弹性耦合效应,外加磁场将对铁磁杆的振动频率产生影响:当铁磁杆的振动位移沿着磁场方向时,其频率减小并出现磁弹性屈曲失稳;当铁磁杆的振动位移垂直于磁场方向时,其频率将会增大．理论模型能够很好地解释已有实验观测的振动频率改变现象．     

竖板表面温度的变化对磁流体动力学流动的影响

在横向磁场作用下,不可压缩的粘性导电流体,流经一个半无限的竖板,完成了壁面温度变化对磁流体动力学流动的分析.假定由粘性耗散和感应磁场产生的热量可以忽略不计.无量纲的控制方程为二维非稳态耦合的非线性方程.结果显示,磁场参数对空气和水的速度有着抑制作用.     

纳米流体在非线性伸展面上粘性流动及其热交换时的相似解

当含金属颗粒的粘性流体(即纳米流体)流过非线性伸展平面时,分析其边界层流动及其热交换.假设伸展速度是到原点距离的幂函数.将偏微分的控制方程及其相应的边界条件,简化为耦合的非线性常微分方程及其相应的边界条件.数值地求解所得到的非线性常微分方程.讨论了各相关参数(即Eckert数Ec,纳米颗粒的固体体积率和非线性伸展参数n)对问题结果的影响,并与先前文献所报道的结果进行了对比.研究了不同类型的纳米颗粒.发现纳米流体的流动特性随着纳米颗粒类型的改变而变化.     

纳米流体流经热分层线性多孔伸展平面时的MHD自然对流及其Lie对称群变换

就不可压缩粘性纳米流体,流经半无限垂直伸展平面并计及热分层时,研究该流体的MHD自然对流和热交换.通过特定形式的Lie对称群变换,即单参数群变换,将所考虑问题的偏微分控制方程变换为常微分方程组.然后,使用基于打靶法的Runge Kutta Gill法进行数值求解.最后得到结论:流场、温度和纳米颗粒体积率受热分层和磁场的影响很显著.     

铁磁性设备补偿磁场的数学模型及其应用

研究用永磁体对铁磁性设备进行磁场补偿的问题,建立了补偿磁场的数学模型.将设备划分成若干个小长方体后,基于磁矩量法建立了数学模型,并对补偿磁场进行拟合.在计算模型中的耦合系数矩阵时,用多个点的平均值作为耦合系数的有效值,提高了计算结果的可靠性和稳定性.并且,针对永磁体距离设备很近时,设备呈现出的非线性磁化特性,通过优化方法求解各个单元的等效磁化率,这种方法不需要知道铁磁材料的磁化曲线和设备结构,便于计算和实际应用.最后,通过实验设计与数值计算,得到了永磁体对设备进行补偿的磁场分布,模型计算结果与实际测量数据误差11%以内,这说明该模型能够满足工业要求,具有实际应用价值.     

Inclusion of interactions in mathematical modelling of implant assisted magnetic drug targeting

Drug delivery technologies are an important area within biomedicine. Targeted drug delivery aims to reduce the undesired side effects of drug usage by directing or capturing the active agents near a desired site within the body. This is particularly beneficial in, for instance, cancer chemotherapy, where the side effects of general (systemic) drug administration can be severe.One approach to targeted drug delivery uses magnetic nanoparticles as the constituents of carriers for the desired active agent. Once injected into the body, the behaviour of these magnetic carriers can be influenced and controlled by magnetic fields. In implant assisted magnetic drug targeting systems a magnetic implant, typically a stent, wire or spherical seed can be used to target sites deep within the body as the implant acts as a focus for the resulting magnetic force. This can be easily understood as the force depends on the gradient of the magnetic field and the gradient near the implant is large.In designing such a system many factors need to be considered including physical factors such as the size and nature of the implants and carriers, and the fields required. Moreover, the range of applicability of these systems in terms of the regions of the vasculature system, from low blood velocity environments, such as capillary beds to higher velocity arteries, must be considered. Furthermore, assessment criteria for these systems are needed. Mathematical modelling and simulation has a valuable role to play in informing in vitro and in vivo experiments, leading to practical system design.Specifically, the implant assisted magnetic drug targeting systems of Avilés, Ebner and Ritter are considered within this review, and two dimensional mathematical modelling is performed using the open source C++ finite volume library OpenFOAM. In the first system treated, a large ferromagnetic particle is implanted into a capillary bed as a seed to aid collection of single domain nanoparticles (radius 20-100 nm). The Langevin function is used to calculate the magnetic moment of the particles, and the model is further adapted to treat the agglomeration of particles known to occur in these systems. This agglomeration can be attributed to interparticle interactions and here the magnetic dipole-dipole and hydrodynamic interactions for two mutually interacting nanoparticles are modelled, following Mikkelsen et al. who treated two particle interactions in microfluidic systems, with low magnetic field (0.05 T). The resulting predicted performance is found to both increase and decrease significantly depending on initial positions of the particles. Secondly, a ferromagnetic, coiled wire stent is implanted in a large arterial vessel. The magnetic dipole-dipole and hydrodynamic interactions for multiple particles are included. Different initial positions are considered and the system performance is assessed. Inclusion of these interactions yields predictions that are in closer agreement with the experimental results of Avilés et al. We conclude that the discrepancies between the non interacting theoretical predictions and the corresponding experimental results can (as suggested by Avilés et al.) be largely attributed to interparticle interactions and the consequent agglomeration.     

Biomagnetic viscoelastic fluid flow over a stretching sheet

Of concern in this paper is an investigation of biomagnetic flow of a non-Newtonian viscoelastic fluid over a stretching sheet under the influence of an applied magnetic field generated owing to the presence of a magnetic dipole. The viscoelasticity of the fluid is characterised by Walter’s B fluid model. The applied magnetic field has been considered to be sufficiently strong to saturate the ferrofluid. The magnetization of the fluid is considered to vary linearly with temperature as well as the magnetic field intensity. The theoretical treatment of the physical problem consists of reducing it to solving a system of non-linear coupled differential equations that involve six parameters, which are solved by developing a finite difference technique. The velocity profile, the skin-friction, the wall pressure and the rate of heat transfer at the sheet are computed for a specific situation. The study shows that the fluid velocity increases as the rate of heat transfer decreases, while the local skin-friction and the wall pressure increase as the magnetic field strength is increased. It is also revealed that fluid viscoelasticity has an enhancing effect on the local skin-friction. The study will have an important bearing on magnetic drug targeting and separation of red cells as well as on the control of blood flow during surgery.     

A 3D non-Newtonian fluid-structure interaction model for blood flow in arteries

The mathematical modelling and numerical simulation of the human cardiovascular system is playing nowadays an important role in the comprehension of the genesis and development of cardiovascular diseases. In this paper we deal with two problems of 3D modelling and simulation in this field, which are very often neglected in the literature. On the one hand blood flow in arteries is characterized by travelling pressure waves due to the interaction of blood with the vessel wall. On the other hand, blood exhibits non-Newtonian properties, like shear-thinning, viscoelasticity and thixotropy. The present work is concerned with the coupling of a generalized Newtonian fluid, accounting for the shear-thinning behaviour of blood, with an elastic structure describing the vessel wall, to capture the pulse wave due to the interaction between blood and the vessel wall. We provide an energy estimate for the coupling and compare the numerical results with those obtained with an equivalent fluid-structure interaction model using a Newtonian fluid.     

Modeling the Sedimentation of Red Blood Cells in Flow under Strong External Magnetic Body Force Using a Lattice Boltzmann Fictitious Domain Method

Experimental observations show that a strong magnetic field has a dramatic influence on the sedimentation of RBCs, which motivates us to model the sedimentation of red blood cell (RBC) under strong external magnetic body force. To model the sedimentation of a RBC in a square duct and a circular pipe, a recently developed technique derived from the lattice Boltzmann and the distributed Lagrange multiplier/fictitious domain methods (LBM-DLM/FD) is extended to employ the mesoscopic network model for simulations of the sedimentation of a RBC in flow. The flow is simulated by the LBM with a strong magnetic body force, while the network model is used for modeling RBC deformation. The fluid-RBC interactions are enforced by the Lagrange multiplier. The sedimentation of RBC in a square duct and a circular pipe is simulated, which demonstrates the developed method's capability to model the sedimentation of RBCs in various flows. Numerical results illustrate that the terminal settling velocity increases incrementally with the exerted body force. The deformation of RBC has a significant effect on the terminal settling velocity due to the change in the frontal area. The larger the exerted force, the smaller the frontal area and the larger the RBC deformation become. Additionally, the wall effect on the motion and deformation of RBC is also investigated.     

Open-surface MHD flow over a curved wall in the 3-D thin-shear-layer approximation

3-D thin-shear-layer equations for flows of conducting fluids in a magnetic field have been derived in orthogonal body-oriented coordinates and then applied to the analysis of MHD open-surface flows over a curved wall. Unlike the classic boundary-layer-type equations, present ones permit information to be propagated upstream through the induced magnetic field. Another departure from the classic theory is that the normal momentum equation keeps the balance between the pressure gradient term, and those related to gravity, centrifugal forces, and Lorentz force. Thus, the normal pressure variations are allowed. The model describes basic 3-D effects due to the wall curvature and spatial variations of the applied magnetic field. As a particular case, equations for flows with rotational symmetry have been derived. Numerical calculations were performed for open-surface flows over a body of revolution under conditions relevant to a fusion reactor (Hartmann number is 8500). Some specific flow patterns, such as flow thickening and spiral-type flows, have been observed and discussed. A special attention has been paid to the analysis of the magnetic propulsion as a tool for the active flow control by applying an electric current. It has been shown that depending on the applied current, the axial pressure gradient can act as an adverse pressure gradient or propulsion force.     

On the refined modeling of the force distribution in a bistable magnetoelastic energy harvesting system due to a magnetic field

Abstract: The problem of a bistable magnetoelastic beam under base excitation was discussed in [1] under the aspect of chaotic behaviour in mechanical systems. Three decades later the system was used in [2] to design an energy harvesting system which performs well under harmonic excitation for a broad range of excitation frequencies due to its bistability. The initial modeling was tailored to obtain a model with one degree of freedom based on the assumption that the magnetic force acts on the beam tip only. A more appropriate model can be found when considering a distributed force along the beam. The authors present the force distribution on a ferromagnetic beam due to the magnetic field of two permanent magnets. A semi-analytic method is used to compute the magnetic field. The force distribution can in future be used to derive a refined nonlinear dynamical model for the ferromagnetic elastic beam. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of particles movement in cellular flows under the influence of magnetic forces

A numerical model of particle motion in fluid flow under the influence of hydrodynamic and magnetic forces is presented. As computational tool, a flow solver based on the Boundary Element Method is used. The Euler-Lagrange formulation of multiphase flow is considered. In the case of a particle with a magnetic moment in a nonuniform external magnetic field, the Kelvin body force acts on a single particle. The derived Lagrangian particle tracking algorithm is used for simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient, added mass and magnetophoretic force. As a benchmark test case the magnetite particle motion in cellular flow field of water is computed with and without the action of the magnetic force. The effect of the Kelvin force on particle motion and separation from the main flow is studied for a predefined magnetic field and different values of magnetic flux density. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimum design of compressive residual stress field caused by ultrasonic surface rolling with a mathematical model

Compressive residual stress fields induced by ultrasonic surface rolling process play a key role in determining the fatigue performance of machine parts. The present work is an analytical approach to conducting optimum design of this field to obtain an optimum fatigue resistance. Thus, a mathematical model was presented to predict residual stresses based on circular and elliptical Hertz contact areas. Moreover, to validate the proposed analytical approach, experimental verification was carried out on 18CrNiMo7-6 steel. Analytic solutions were derived from the mathematical model and optimum characteristic parameters were obtained by investigating the characteristic parameters in this field, such as surface residual stress, maximum residual stress and its depths. Results showed that increasing the total force, Hertz contact area and ratio of the radius of tool tip to that of target body could significantly enhance the peak of compressive residual stress and its depth.     

Mathematical modeling of the receptor-mediated endocytosis process of targeted therapeutic agents in drug delivery systems

In this paper, we propose mathematical models to describe receptor-mediated endocytosis processes. One is a stochastic differential model for the agent-target binding process. The mean extinction time and a standard variation over time profile are evaluated. The other is an age-structured model for demonstrating endocytosis and lysosome processes. A targeted drug delivery system has a complex process in how it is to deliver drug molecules in terms of administration, transportation in blood and across membranes to intracellular space, and inhibition to microtubule polymerization. In particular, receptor-mediated endocytosis of targeted therapeutic agents, such as antibody drug conjugates or ligand-targeted liposome encapsulated nanoparticles, is a key step in understanding the drug delivery mechanism. We discuss stochastic quasi steady state approximation when agent-target complex does not appreciably vary compared with the free agents. This reduces the number of the systems and the parameters; however, an initial time phase cannot be captured. In addition, we discuss the strengths and weaknesses when the age-structured model induces the reduced model compared with the full model that considers endocytosis and lysosome processes. If the total mean retention time until payload release in intracellular space is known, then the age-structured model with the Erlang distribution may fairly predict data of the released payload over time profile with far fewer parameters; however, induced compartments lose their physical meaning and describe only a delay.