Exact Solutions for the Flow of Fractional Maxwell Fluid in Pipe-Like Domains

This paper presents an analysis of unsteady flow of incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The fluid motion is created by the inner cylinder that applies a longitudinal time-dependent shear stress and the outer cylinder that is moving at a constant velocity. The velocity field and shear stress are determined using the Laplace and finite Hankel transforms. Obtained solutions are presented in terms of the generalized G and R functions. We also obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of generalized solutions. The influence of different parameters on the velocity field and shear stress is also presented using graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.     

Influence of bioconvection on Maxwell nanofluid flow with the swimming of motile microorganisms over a vertical rotating cylinder

In recent times, bioconvection phenomenon through the use of nanomaterials has encountered significant manufacturing and technical applications. Bioconvection has several applications in bio-micro-system, due to the enhancement in mass transformation and mixing, which are crucial problems in different micro-systems. The aim of current article is to scrutinize the bioconvection phenomenon in 3D Maxwell nanofluid flow with useful characteristics of mixed convection, activation energy, motile microorganisms and solutal boundary conditions. The flow problem focused on the related laws, outcomes in a series of PDEs which have also been delayed in ODE's structure. The numerical method based on a shooting technique is applied to implement a bvp4c solver using the computational software MATLAB. Shooting tactic is utilized to construct the numerical arrangement of subsequent problem. The mathematical division for the local Nusselt number, the motile microorganism's number, and the local Sherwood number is provided when applying different characteristics to the concerned parameters. The hypothetical simulations mentioned may be more successful in enhancing thermal extrusion mechanisms and solar energy structures. The numerical results regarding flow, thermal field, solutal field and concentration of microorganisms are revealed for growing values of interesting parameters. Furthermore, it is inspected that velocity field dwindles with enlarged variation of Maxwell fluid parameter. It is analyzed that radial velocity of Maxwell nanofluid reduces for larger magnitude of mixed convection parameter. Additionally, temperature profile of species upsurges for larger values of thermal stratification Biot number. Moreover, it is inspected that concentration of species decline for higher estimation of Lewis number while enhanced for activation energy parameter. Microorganisms concentration field of Maxwell nanofluid is detected to be an declining function of Peclet number and bioconvection Lewis number. Angorgeous concurrence is obtained when our accomplished numerical results are compared with an already existed magnitudes in limiting condition; hence dependable results are being eliminated.     

MHD Maxwell flow modeled by fractional derivatives with chemical reaction and thermal radiation

Heat transfer in a time-dependent flow of incompressible viscoelastic Maxwell fluid induced by a stretching surface has been investigated under the effects of heat radiation and chemical reaction. The magnetic field is applied perpendicular to the direction of flow. Velocity, temperature, and concentration are functions of z and t for the modeled boundary-layer flow problem. To have a hereditary effect, the time-fractional Caputo derivative is incorporated. The pressure gradient is assumed to be zero. The governing equations are non-linear, coupled and Boussinesq approximation is assumed for the formulation of the momentum equation. To solve the derived model numerically, the spatial variables are discretized by employing the finite element method and the Caputo-time derivatives are approximated using finite difference approximations. It reveals that the fractional derivative strengthens the flow field. We also observe that the magnetic field and relaxation time suppress the velocity. The lower Reynolds number enhances the viscosity and thus motion weakens slowly. The velocity initially decreases with increasing unsteadiness parameter δ. Temperature is an increasing function of heat radiation parameter but a decreasing one for the volumetric heat absorption parameter. The increasing value of the chemical reaction parameter decreases concentration. The Prandtl and Schmidt numbers adversely affect the temperature and concentration profiles respectively. The fractional parameter changes completely the velocity profiles. The Maxwell fluids modeled by the fractional differential equations flow faster than the ordinary fluid at small values of the time t but become slower for large values of the time t.     

Spin-dependent transverse force on a vortex light beam in an inhomogeneous medium

Spin-dependent effects on vortex light beams propagating in an inhomogeneous medium are demonstrated by solving the full three-component field Maxwell equations using the perturbation analysis. It is found that the hybrid Laguerre–Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams in a cylindrical graded-index medium is investigated. It is shown that the vortex light beam undergoes an additional transverse force acting differently on circular polarized beams with opposite handedness. The wave shape variation with distance taking into account the spin–orbit and nonparaxial effects is analyzed. Effect of long-term periodical revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated.     

Effects of transpiration on unsteady MHD flow of an upper convected Maxwell （UCM） fluid passing through a stretching surface in the presence of a first order chemical reaction

The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell （UCM） model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration （suction） and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration （suction） and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.     

Study of electromagnetic field surface states in photonic crystals using the finite-difference method

Bulletin of the Lebedev Physics Institute - The properties of electromagnetic field surface states in globular photonic crystals are analyzed using numerical solution of Maxwell equations by the...     

Magnetohydrodynamic Stagnation Point Flow of a Maxwell Nanofluid with Variable Conductivity

This article reports the simultaneous properties of variable conductivity and chemical reaction in stagnation point flow of magneto Maxwell nanofluid.The Buongiorno's theory has been established to picture the inducement of Brownian and thermophrotic diffusions effects.Additionally,the aspect of heat sink/source is reported.The homotopic analysis method(HAM) has been worked out for the solution of nonlinear ODEs.The behavior of inferential variables on the velocity,temperature,concentration and local Nusselt number for Maxwell nanofluid are sketched and discussed.The attained outcomes specify that both the temperature and concentration of Maxwell fluid display analogous behavior,while the depiction of Brownian motion is quite conflicting on both temperature and concentration fields.It is further noted that the influence of variable thermal conductivity on temperature field is similar to that of Brownian motion parameter.Moreover,for the confirmation of our study comparison tables are reported.     

Multi-layer flows of immiscible fractional Maxwell fluids in a cylindrical domain

Laminar unsteady multilayer axial flows of fractional immiscible Maxwell fluids in a circular cylinder are investigated. The flow of fluids is generated by a time-dependent pressure gradient in the axial direction and by the translational motion of a cylinder along his axis. The considered mathematical model is based on the fractional constitutive equation of Maxwell fluids with Caputo time-fractional derivatives. Analytical solutions for the fractional differential equations of the velocity fields with boundary and interfaces conditions have been determined by using the Laplace transform coupled with the Hankel transform of order zero and the Weber transform of order zero. The influence of the memory effects on the motion of the fluid has been investigated for the particular case of three fractional Maxwell fluids. It is found that for increasing values of the fractional parameter the fluid velocity is decreasing. The memory effects have a stronger influence on the velocity of the second layer.     

Cylindrical electromagnetic waves in a nonlinear nondispersive medium: Exact solutions of the Maxwell equations

The excitation and propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium are analyzed. It is assumed that the medium lacks a center of symmetry and that the dependence of the electric displacement on the electric field can be approximated by an exponential function. For this case, a method for integrating the system of the Maxwell equations is proposed. Exact solutions to a set of nonlinear electromagnetic field equations are obtained by this method. It is shown that nonlinear effects described by these solutions can become apparent under experimental conditions.     

Effect of slip boundary condition on flow and heat transfer of a double fractional Maxwell fluid

The purpose of the present paper is to investigate the flow and heat transfer of a double fractional Maxwell fluid with a second order slip model. The fractional governing equations are solved numerically by using the finite difference method. By comparing the analytical solutions of special boundary conditions, the validity of the present numerical method is examined. The effects of the two slip parameters and the fractional parameters on the velocity and temperature distribution are presented graphically and discussed. The results reveal that the fractional Maxwell fluid exhibits a stronger viscosity or elasticity for different fractional parameters, and the oscillation phenomenon will gradually decrease as expected with an increase in slip parameters.     

Non-relativistic approximate numerical ideal-magneto-hydrodynamics of (1+1D) transverse flow in Bjorken scenario

In this study, we investigate the impact of the magnetic field on the evolution of the transverse flow of QGP matter in the magneto-hydrodynamic (MHD) framework. We assume that the magnetic field is perpendicular to the reaction plane and then we solve the coupled Maxwell and conservation equations in (1+1D) transverse flow, within the Bjorken scenario. We consider a QGP with infinite electrical conductivity. First, the magnetic effects on the QGP medium at mid-rapidity are investigated at leading order; then the time and space dependence of the energy density, velocity and magnetic field in the transverse plane of the ideal magnetized hot plasma are obtained.     

Unsteady MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid with Cattaneo heat flux and different particle shapes

The paper aims to investigate the unsteady natural convection flow and heat transfer of fractional Maxwell viscoelastic nanofluid in magnetic field over a vertical plate. The effect of nanoparticle shape is first introduced to the study of fractional Maxwell viscoelastic nanofluid. Fractional shear stress and Cattaneo heat flux model are applied to construct the governing boundary layer equations of momentum and energy, which are solved numerically. The quantities of physical interest are graphically presented and discussed in detail. It is found that particle shape and fractional derivative parameters have profound influence on the flow and heat transfer.     

外加磁场微波等离子推力器内流场数值模拟

为了提高微波等离子推力器性能，改善等离子体对电磁波能量的吸收状况，提高核心区温度，提出外加磁场的方案，并对热等离子体进行了数值模拟.假设局域热平衡条件，采用Navier-Stokes，Maxwell和Saha方程，利用压力修正的半隐格式和时域有限差分求解方法，建立了径向磁镜场下推力器内等离子体流场的数值计算模型.数值模拟结果表明：外加磁场后的磁感应强度小于0.5 T时，推力器内热等离子体核心区最高温度随磁感应强度的增加而迅速提高.外加磁场后的磁感应强度大于0.5 T时，核心区最高温度随磁感应强度的增加而缓慢提高.磁感应强度为0.5 T时，热等离子体核心区最高温度与不加磁场相比提高了24%.外加磁场对等离子体流场速度分布影响不大. 关键词： 等离子体模拟 等离子体相互作用 等离子体流动     

FDTD方法分析高功率微波对大气的电离与击穿

 应用麦克斯韦方程和电子流体方程,利用时域有限差分方法(FDTD)计算模拟了高功率微波(HPM)对大气的电离与击穿;该方法用瞬时电场代替等效电场,时刻更新大气电离击穿过程中的电离频率和碰撞频率,消除了近似解析法未考虑大气电离击穿过程中电场幅度衰减而引起的误差,计算得到击穿阈值大小随海拔高度的变化趋势与文献所得的变化趋势相吻合,其值略大于近似解析解;并通过仿真计算分析了HPM脉冲幅值、脉宽以及海拔高度等参数对大气击穿的影响。     

Transient electro-osmotic flow of generalized Maxwell fluids in a straight pipe of circular cross section

The transient electro-osmotic flow of a generalized Maxwell fluid with fractional derivative in a narrow capillary tube is examined. With the help of an integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson-Boltzmann equation and the Navier-Stokes equation. It was shown that the distribution and establishment of the velocity consists of two parts, the steady part and the unsteady one. The effects of relaxation time, fractional derivative parameter, and the Debye-Hückel parameter on the generation of flow are shown graphically and analyzed numerically. The velocity overshoot and oscillation are observed and discussed.     

FDTD结合DFT分析宽频高功率微波大气传播

联立麦克斯韦方程与电子流体方程,用时域有限差分法(FDTD)模拟高斯型和阻尼正弦型等宽频高功率微波(HPM)的大气传播.在每个时间网格上,根据窄带脉冲的电子速度,通过离散傅立叶变换(DFT)方法求解出宽频脉冲的等效电场,将等效电场和压强代入电离参数公式,使电离参数随空间网格不断更新,提高计算准确性.结果表明,宽频HPM脉冲幅值、脉宽以及海拔高度等参数对大气击穿有明显的影响;大气击穿导致尾蚀效应;随着传播距离的增加,宽频HPM脉冲的尾部衰减加剧,脉宽缩短,引起宽频脉冲的频谱出现展宽、分裂及中心频率移动等现象.     

Axisymmetric convection flow of fractional Maxwell fluid past a vertical cylinder with velocity slip and temperature jump

A novel finite volume method is developed to investigate the axisymmetric convection flow and heat transfer of fractional viscoelastic fluid past a vertical cylinder. Fractional cylindrical governing equations are formulated by fractional Maxwell model and generalized Fourier's law. The velocity slip and temperature jump boundary conditions are considered across the fluid-solid interface. Numerical results are validated by exact solutions of special case with source terms. The effects of fractional derivative parameter and boundary condition parameters on flow and heat transfer characteristics are discussed. The viscoelastic fluid performs evident shear thickening property in the fractional Maxwell constitutive relation. Moreover, the boundary condition parameters have remarkable influence on velocity and temperature distributions.     

MHD swirling flow and heat transfer in Maxwell fluid driven by two coaxially rotating disks with variable thermal conductivity

We develop a mathematical modeling for an electrically conducting non-Newtonian Maxwell fluid flow occurring between two coaxially parallel stretchable rotating disks at constant distant apart. The pressure and heat transfer analysis is carried out subject to the effects of axial magnetic field and temperature dependent thermal conductivity. The stretching and rotating rates of both disks are assumed different from each other. The two diverse phenomena, such as, when both disks are rotating with different angular velocities in the same as well as in the opposite directions are discussed. The similarity procedure adopted by von Kármán is utilized to reduce the governing momentum and energy equations into nonlinear ordinary differential equations. The solution of the governing problem is obtained numerically using bvp4c scheme in Matlab. The effects of active parameters including stretching rates, Deborah number, magnetic number, Prandtl number, thermal conductivity parameter and Reynolds number are examined for same as well as opposite rotation direction for radial, azimuthal, and axial flows, pressure and temperature fields. The classical flow pattern happening between the disks is significantly altered by the stretching action which is a main physical significances of this study. The azimuthal flow is observed higher for the same direction of disks rotation as compared to opposite disks rotation. The pressure field drops near the lower disk with increasing values of Reynolds number. The role of thermal conductivity parameter is quite useful to enhance the fluid temperature.     

Simultaneous features of Wu's slip,nonlinear thermal radiation and activation energy in unsteady bio-convective flow of Maxwell nanofluid configured by a stretching cylinder

This continuation deals with the bioconvection flow of magnetized Maxwell nanofluid over a stretched cylinder in presence of slip effects. The novel features of activation energy and thermal radiation are also encountered to analyze the flow. The higher order slip relations are introduced to inspect the thermal flow problem. The flow model is developed in terms of dimensionless equations via appropriate variables. The numerical simulations are presented with shooting scheme by using MATLAB software. The physical outcomes of interesting parameters are visualized. The observations show that velocity profile reduces with unsteady parameter, curvature constant and second order slip factor. The temperature profile enhanced with first order velocity slip parameter and curvature constant. Moreover, nanofluid concentration reduces with Lewis number and Brownian constant.