MHD flow study of viscous fluid through a complex wavy curved surface due to biomimetic propulsion under porosity and second-order slip effects

The steady laminar flow of viscous fluid from a curved porous domain under a radial magnetic field is considered. The fluid flow by a curved domain is due to peristaltic waves present at the boundary walls. The whole analysis is based on porosity(Darcy number) effects. Moreover, the effects of second-order slip on the rheology analysis are also discussed. Due to the complex nature of the flow regime, we have governed the rheological equations by using curvilinear coordinates in the fixed frame. The physical influence of magnetic(Hartmann number) and porosity(Darcy number)parameters on the rheological features of peristaltic transportation are argued in detailed(in the wave frame). Additionally, in the current study, the complex wavy pattern on both boundary walls of the channel is used. The whole rheological study is based on ancient, but medically valid,assumptions of creeping phenomena and long wavelength assumptions. Analytical solutions of the governing equations are obtained by using the simple integration technique in Mathematica software 11.0. The core motivation of the present analysis is to perceive the physical influence of embedded parameters, such as the dimensionless radius of the curvature parameter, magnetic parameter, porosity parameter, different amplitude ratios of complex peristaltic waves, first-and second-order slip parameters, on the axial velocity, pressure gradient, local wall shear stress,tangential component of the extra-stress tensor, pumping and trapping phenomena.     

Non-linear peristaltic transport of a Newtonian fluid in an inclined asymmetric channel through a porous medium

Peristaltic transport of an incompressible viscous fluid in an inclined asymmetric channel through a porous medium is studied under long-wavelength and low-Reynolds number assumptions. The flow is examined in a wave frame of reference moving with the velocity of the wave. The analytical solution has been obtained in the form of a stream function from which the axial velocity and pressure gradient have been derived. The results for the pressure drop and shear stress have also been computed numerically. The effects of various physical parameters are discussed through graphs and the phenomenon of trapping is also discussed. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.     

Effects of magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel

The effects of both magnetic field and wall slip conditions on the peristaltic transport of a Newtonian fluid in an asymmetric channel are studied analytically and numerically. The channel asymmetry is generated by propagation of waves on the channel walls travelling with different amplitudes, phases but with the same speed. The long wavelength and low Reynolds number assumptions are considered in obtaining solution for the flow. The flow is investigated in a wave frame of reference moving with velocity of the wave. Closed form expressions have been obtained for the stream function and the axial velocity component in fixed frame. The effects of phase difference, Knudsen number and magnetic field on the pumping characteristics and velocity field are discussed. Several known results of interest are found to follow as particular cases of the solution of the problem considered.     

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.     

Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

Influence of partial slip on the peristaltic flow in a porous medium

In this paper, the slip effects are discussed on the peristaltic flow of a viscous fluid in a porous medium. A long wavelength approximation is used in the flow modelling. The solutions for stream function and axial velocity are constructed by employing the Adomian decomposition method. Numerical integration has been used for the pumping and trapping phenomena. Graphs illustrate the physical behavior. It is noted that the size of the trapped bolus decreases and its symmetry disappears for large values of the slip parameter. Further, the peristaltic pumping rate decreases by increasing the slip parameter.     

Analysis of magnetohydrodynamic flow of a fractional viscous fluid through a porous medium

The aim of this paper is to investigate the exact general solutions of the incompressible viscous fluid flow by using the time-fractional Caputo–Fabrizio derivative. The flow of the fluid is subject to the motion of a plane wall, embedded in a porous medium under the influence of magnetic field. The corresponding non-dimensional governing fractional differential equation with appropriate initial and boundary conditions is solved by means of integral transforms namely, Laplace and Fourier transforms. Solutions are expressed as a sum of steady and transient parts, for the sinusoidal oscillations of the plane wall. The influence of involved physical parameters are discussed graphically. Specifically, it has been observed that the effective permeability K_eff reduces the time taken to reach the steady state.     

An analytical and numerical study of peristaltic transport of a Johnson-Segalman fluid in an endoscope

In the present study, we discuss the peristaltic flow of a Johnson-Segalman fluid in an endoscope. Perturbation, homotopy, and numerical solutions are found for the non-linear differential equation. The comparative study is also made to check the validity of the solutions. The expressions for pressure rise frictional forces, pressure gradient, and stream lines are presented to interpret the behavior of various physical quantities of the Johnson-Segalman fluid.     

An alytical and numerical study of peristaltic transport of a Johnson-Segalman fluid in an endoscope

In the present study, we discuss the peristaltic flow of a Johnson-Segalman fluid in an endoscope. Perturbation, homotopy, and numerical solutions are found for the non-linear differential equation. The comparative study is also made to check the validity of the solutions. The expressions for pressure rise frictional forces, pressure gradient, and stream lines are presented to interpret the behavior of various physical quantities of the Johnson-Segalman fluid.     

Transport of Jeffrey fluid in a rectangular slit of the microchannel under the effect of uniform reabsorption and a porous medium

This research explores the transport of a Jeffrey fluid through a permeable slit of microchannel under the effect of a porous medium and constant reabsorption. Physical laws of fluid mechanics are used to study the flow in a cross-sectional area of a narrow slit which generates a highly nonlinear system of partial differential equation with nonhomogeneous boundary conditions. To solve the complex boundary value problem; a recursive (Langlois) approach is used and explicit expressions for velocity, pressure, stream function, flux, shear stress and fractional reabsorption are calculated. It is noticed that the flow rate at the centre line of slit and shear stress on the walls of slit decay due to the presence of porous medium and viscoelastic fluid parameters. It is also quantitatively observed that more pressure is required for the fluid flow when the slit is filled with a porous medium and reabsorption on the walls is constant. The mathematical results of the present research have significant importance in the field of biofluid mechanics and medical industry, therefore the application of a diseased rat kidney is also included in this research: and reabsorption velocities in the case of a diseased and a healthy rat kidney are calculated with the effects of a porous medium and constant re-absorption.     

Three-dimensional absolute and convective instabilities in mixed convection of a viscoelastic fluid through a porous medium

By using the mathematical formalism of absolute and convective instabilities we study the nature of unstable three-dimensional disturbances of viscoelastic flow convection in a porous medium with horizontal through-flow and vertical temperature gradient. Temporal stability analysis reveals that among three-dimensional (3D) modes the pure down-stream transverse rolls are favored for the onset of convection. In addition, by considering a spatiotemporal stability approach we found that all unstable 3D modes are convectively unstable except the transverse rolls which may experience a transition to absolute instability. The combined influence of through-flow and elastic parameters on the absolute instability threshold, wave number and frequency is then determined, and results are compared to those of a Newtonian fluid.     

基于Biot-喷射流统一模型Maxwell流体饱和孔隙介质中的弹性波

推广Biot-Tsiklauri声学模型的同时借鉴Dvorkin和Nur的工作,建立了具有任意孔径分布并顾及喷射流动机制的非牛顿流体饱和孔隙介质声学模型,研究了非牛顿流体(Maxwell流体)饱和孔隙介质中的弹性波的衰减和频散特性.着重讨论充孔隙Maxwell流体的非牛顿流效应对弹性波的频散和衰减的影响.研究表明,饱和流体的非牛顿流效应和喷射流动机制均是引起弹性波波频散和衰减的重要因素.依据非牛顿流体(Maxwell流体)饱和各向同性孔隙介质的Biot-喷射流声学模型,喷射流动只影响纵波的频散和衰减,而饱和流体的非牛顿流效应不仅影响纵波,而且还影响横波的频散和衰减.     

磁性液体表观密度随磁场变化测量仪的研制

利用自制的磁性液体研制出测量固、液两相胶体溶液磁性液体表现密度的测量装置并给出了测量方法和测量原理．该装置既能测量磁性液体中不同液层的表观密度，也能测量磁性液体中某点的表观密度随磁场变化的规律．     

MHD peristaltic motion of Johnson-Segalman fluid in a channel with compliant walls

A mathematical model for magnetohydrodynamic (MHD) flow of a Johnson-Segalman fluid in a channel with compliant walls is analyzed. The flow is engendered due to sinusoidal waves on the channel walls. A series solution is developed for the case in which the amplitude ratio is small. Our computations show that the mean axial velocity of a Johnson-Segalman fluid is smaller than that of a viscous fluid. The variations of various interesting dimensionless parameters are graphed and discussed.     

The influence of heat transfer and magnetic field on peristaltic transport of a Newtonian fluid in a vertical annulus: Application of an endoscope

This Letter discusses the influence of heat transfer and magnetic field on the peristaltic flow of Newtonian fluid in a vertical annulus under a zero Reynolds number and long wavelength approximation. The inner tube is uniform, rigid, while the outer tube has a sinusoidal wave traveling down its wall. The flow is investigated in a wave frame of reference moving with velocity of the wave. Numerical calculations are carried out for the pressure rise and frictional forces. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail.     

Stability of thermal convection of an Oldroyd-B fluid in a porous medium with Newtonian heating

A linear stability analysis determining the onset of oscillatory convection of an Oldroyd-B fluid in a bounded two-dimensional rectangular porous medium generated by Newtonian heating is conducted. Influences of viscoelastic parameters and Biot number on the onset of oscillatory convection, preferred modes and patterns of disturbed temperature contours are discussed.     

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通过数值模拟及实验研究了润湿性及磁场对液态金属膜流流动状态的影响.首先,通过数值模拟研究了润湿性对膜流流动状态的影响.结果表明,当润湿性不好时,液态金属膜流容易发展为溪状流而不能完全覆盖底壁,入口膜厚较薄时更易发展为溪状流;在入口膜厚及其它情况相同时,密度越小越易发展为溪状流.其次,研究了磁场对膜流流动状态的影响.结果表明,槽道与流体润湿性不好时,有磁场情况下液态金属膜流覆盖底壁的区域较无磁场时增加,强磁场对膜流的湍流有抑制作用.最后,液态金属膜流实验结果表明,润湿性不好时,镓铟锡合金膜流容易收缩发展为溪状流,这与数值模拟的结果是一致的.上述研究结果对磁约束聚变堆液态第一壁的设计具有指导意义.     

润湿性及磁场对液态金属自由表面膜流流动状态的影响

通过数值模拟及实验研究了润湿性及磁场对液态金属膜流流动状态的影响。首先,通过数值模拟研究了润湿性对膜流流动状态的影响。结果表明,当润湿性不好时,液态金属膜流容易发展为溪状流而不能完全覆盖底壁,入口膜厚较薄时更易发展为溪状流;在入口膜厚及其它情况相同时,密度越小越易发展为溪状流。其次,研究了磁场对膜流流动状态的影响。结果表明,槽道与流体润湿性不好时,有磁场情况下液态金属膜流覆盖底壁的区域较无磁场时增加,强磁场对膜流的湍流有抑制作用。最后,液态金属膜流实验结果表明,润湿性不好时,镓铟锡合金膜流容易收缩发展为溪状流,这与数值模拟的结果是一致的。上述研究结果对磁约束聚变堆液态第一壁的设计具有指导意义。     

Dual solutions in boundary layer flow of Maxwell fluid over a porous shrinking sheet

An analysis is carried out for dual solutions of the boundary layer flow of Maxwell fluid over a permeable shrinking sheet. In the investigation, a constant wall mass transfer is considered. With the help of similarity transformations, the governing partial differential equations（PDEs） are converted into a nonlinear self-similar ordinary differential equation（ODE）. For the numerical solution of transformed self-similar ODE, the shooting method is applied. The study reveals that the steady flow of Maxwell fluid is possible with a smaller amount of imposed mass suction compared with the viscous fluid flow. Dual solutions for the velocity distribution are obtained. Also, the increase of Deborah number reduces the boundary layer thickness for both solutions.     

Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium

This study has compared the convection heat transfer of Water-based fluid flow with that of Water-Copper oxide (CuO) nanofluid in a sinusoidal channel with a porous medium. The heat flux in the lower and upper walls has been assumed constant, and the flow has been assumed to be two-dimensional, steady, laminar, and incompressible. The governing equations include equations of continuity, momentum, and energy. The assumption of thermal equilibrium has been considered between the porous medium and the fluid. The effects of the parameters, Reynolds number and Darcy number on the thermal performance of the channel, have been investigated. The results of this study show that the presence of a porous medium in a channel, as well as adding nanoparticles to the base fluid, increases the Nusselt number and the convection heat transfer coefficient. Also the results show that As the Reynolds number increases, the temperature gradient increases. In addition, changes in this parameter are greater in the throat of the flow than in convex regions due to changes in the channel geometry. In addition, porous regions reduce the temperature difference, which in turn increases the convective heat transfer coefficient.