Effects of temperature dependent viscosity on peristaltic flow of a Jeffrey-six constant fluid in a non-uniform vertical tube

This paper deals with the influence of heat transfer and temperature dependent viscosity on peristaltic flow of a Jeffrey-six constant fluid. The two-dimensional equations of Jeffrey-six constant fluid are simplified by making the assumptions of long wave length and low Reynolds number. The arising equations are solved for temperature, velocity profile and axial pressure gradient using regular perturbation method and homotopy analysis method. The integration appeared in the pressure rise is treated numerically to find the solution. The expressions for pressure rise, temperature, pressure gradient and stream functions are sketched for various embedded parameters and interpreted. The graphical results are also presented for five different wave shapes.     

Influence of induced magnetic field on peristaltic flow in an annulus

This paper looks at the influence of the induced magnetic field on peristaltic transport through a uniform infinite annulus filled with an incompressible viscous and Newtonian fluid. The present theoretical model may be considered as mathematical representation to the movement of conductive physiological fluids in the presence of the endoscope tube (or catheter tube). The inner tube is uniform, rigid, while the outer tube has a sinusoidal wave traveling down its wall. The flow analysis has been developed for low Reynolds number and long wave length approximation. Exact solutions have been established for the axial velocity, stream function, axial induced magnetic field, current distribution and the magnetic force function. The effects of pertinent parameters on the pressure rise and frictional forces on the inner and outer tubes are investigated by means of numerical integrations, also we study the effect of these parameters on the pressure gradient, axial induced magnetic field and current distribution. The phenomena of trapping is further discussed.     

Effects of heat transfer and space porosity on peristaltic flow in a vertical asymmetric channel

This article discusses the effect of heat transfer on the peristaltic flow of a Newtonian fluid through a porous space in a vertical asymmetric channel. Long wavelength approximation is used to linearize the governing equations. The system of the governing nonlinear PDE is solved by using the perturbation method. The solutions are obtained for the velocity and the temperature fields. 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, frictional forces, and the features of the flow and temperature characteristics are analyzed by plotting graphs and discussed in detail. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Response of multiwall carbon nanotubes to impact loading

Dynamic behaviors of multiwall carbon nanotubes (MWCNTs) with finite length are investigated using an analytical method. Multiple elastic shells and linearized model of van der Waals forces are used for development a comprehensive continuum dynamic model of MWCNTs. By applying Laplace transform, analytical solution for thin and thick MWCNTs under dynamic loading are obtained. Dynamic responses of 3-, 9-, and 11-layer MWCNTs under external pressure shock are examined and accuracy of results are verified by comparison the results with those obtained by numerical methods. Both displacement and stress analysis are performed for layers of MWCNTs and frequencies of oscillations are obtained. Also, effects of axial wave created by external pressure shock are studied in MWCNTs with two-dimensional analyses. Dynamic responses of MWCNTs with initial axial displacement are also proposed and the propagation of the axial wave through the length of tubes is illustrated. Furthermore, wave propagation velocity is found by analysis of time history diagram.     

Non-linear peristaltic flow of a non-Newtonian fluid under effect of a magnetic field in a planar channel

This paper is devoted to the study of peristaltic flow of a fourth grade fluid in a channel under the considerations of long wavelength and low-Reynolds number. The flow is examined in a wave frame of reference moving with velocity of the wave. The analytic solution has been obtained in the form of a stream function from which the axial velocity and axial pressure gradient have been derived. The results for the pressure rise and frictional force per wavelength have also been computed numerically. The computational results indicate that the pressure rise and frictional force per wavelength are increased in case of non-Newtonian fluid when compared with Newtonian fluid. Several graphs of physical interest are displayed and discussed.     

Effect of variable viscosity on the peristaltic transport of a Newtonian fluid in an asymmetric channel

The effect of variable viscosity on the peristaltic flow of a Newtonian fluid in an asymmetric channel has been discussed. Asymmetry in the flow is induced due to travelling waves of different phase and amplitude which propagate along the channel walls. A long wavelength approximation is used in the flow analysis. Closed form analytic solutions for velocity components and longitudinal pressure gradient are obtained. The study also shows that, in addition to the effect of mean flow parameter, the wave amplitude also effect the peristaltic flow. This effect is noticeable in the pressure rise and frictional forces per wavelength through numerical integration.     

Influence of heat and mass transfer on peristaltic flow of a third order fluid in a diverging tube

In the present investigation we have discussed the heat and mass transfer analysis on peristaltic flow of a third order fluid in a diverging tube. The assumption of low Reynolds number and long wavelength have been used to simplify the complicated problem into relatively simple problem. Two types of analytical solutions named as perturbation solution and solution have been evaluated for velocity, temperature and concentration field. The expression for pressure rise and frictional forces are calculated using numerical integration. In addition, the quantitative effects of pressure rise, frictional forces, temperature and concentration profile are displayed graphically. Trapping phenomena is also discussed at the end of the article.     

Effects of an endoscope and magnetic field on the peristalsis involving Jeffrey fluid

This paper looks at the influence of an endoscope on the peristaltic flow of a Jeffrey fluid through tubes. The considered fluid is incompressible and electrically conducting. The governing partial differential equations are modeled. Exact analytic solutions for velocity components and pressure gradient are established under long wavelength assumption. 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.     

Non-linear peristaltic transport of a second-order fluid through a porous medium

The present paper investigates phenomena brought about into the classic peristaltic mechanism by inclusion of non-Newtonian effects through a porous space in a channel. The peristaltic motion of a second-order fluid through a porous medium was studied for the case of a planar channel with harmonically undulating extensible walls. The system of the governing nonlinear PDE is solved by using the perturbation method to second-order in dimensionless wavenumber. The analytic solution has been obtained in the form of a stream function from which the axial pressure gradient has been derived. 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 force. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail.     

Action of an elliptic stamp moving at a constant speed on an elastic half-space : PMM vol. 42, no. 6, 1978, pp 1074–1079

The action of a rigid stamp moving at a constant speed, on the boundary of an elastic half-space, is investigated. It is assumed that the frictional forces between the stamp and the surface of the half-space are absent. The integral equation obtained in [1] yields formulas for the pressure, for the case when the area of contact between the stamp and the half-space has an elliptic form.     

Multiscale simulation for description of rubber friction

The interaction between tire and road generates the transferable forces, which are necessary for driving dynamics and safety. These forces are based on friction between rubber material and pavement surface and depend on the roughness of the pavement, the slip velocity, the contact pressure and the temperature. Based on the finite element method, the friction coefficient is calculated by numerical simulation. The roughness of the pavement surface is described by the height difference correlation function (HDCF), which allows partitioning into different length scales. This multiscale approach is suitable to understand and to evaluate friction phenomena. These phenomena are hysteresis friction based on dissipation inside the rubber material and adhesion friction, which describes the direct bonding between two materials. Given, that the material parameters of rubber highly depend on temperature and the frictional dissipation leads to a warming of the rubber, the provision for these effects is necessary for a realistic desciption of friction. The method allows an understanding of friction phenomena on the micro-scale like the real contact area or the microscopic contact pressure. Also, the temperature distribution inside the tire cross-section can be illustrated. The resulting coefficient of friction is validated by experimental data based on linear friction tests and compared to analytical solutions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equations and interface conditions for acoustic phenomena in porous media

Acoustic phenomena are considered in a porous medium made of a rigid matrix hollowed by a lattice of periodically distributed canals of arbitrary shape, the period of the lattice being small compared with the wave length. If dissipation phenomena are taken into account in the solution of the Navier-Stokes equations at the microscopic level, the averaged acoustic variables satisfy equations analogous to those of acoustics in a fictitious homogeneous dissipative (and possibly anisotropic) medium whose properties are described. Interface phenomena between such a medium and a free fluid are studied. As a result, the interface conditions for the averaged variables on the one hand and the free fluid variables on the other hand are the continuity of pressure and normal velocity. The acoustic impedance of the surface is not a constant.     

The stress-deformed state of a packet of cylindrical shells taking account of friction

We propose a method of determining the contact pressures between the shells in a packet under the influence of nonlinear internal and constant external pressure. Using the equations of the general moment theory of shells we determine the stress-deformed state of a packet of finite cylindrical shells taking account of frictional forces on the contacting surfaces. One table. Bibliography: 10 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 94–98.     

Sound radiation by a plate reinforced by a set of projecting stiffener ribs subjected to a periodic system of forces

There is considered sound radiation by a plate reinforced by a periodic set of projecting stiffener ribs of small wave dimensions. The source of the field is a set of lumped harmonic forces applied to the plate periodically in each transit, where the forces are taken identical in amplitude but with a constant phase shift between adjacent sources. The problem reduces to a quasiregular infinite system of linear algebraic equations, in terms of whose solution the energy fluxes leaving the plate into the fluid are expressed.     

A semianalytical approach to nonlinear fluid film forces of a hydrodynamic journal bearing with two axial grooves

A semianalytical approach to nonlinear fluid film forces of a hydrodynamic journal bearing with two axial grooves under the cavitation boundary condition is proposed. The pressure distribution of the Reynolds equation of a finitely long journal bearing with axial grooves is expressed as a particular solution and a homogeneous solution. The particular solution and the homogeneous solution are separated, respectively, into an additive form and a multiplicative form by the method of separation of variables. The circumferential separable function of the homogeneous solution can be expanded on the basis of the infinite series of trigonometric functions. The pressure distribution of the particular solution is obtained by the Sommerfeld transformation. The termination positions of the fluid film are determined by the continuity condition. The analytical expressions for the nonlinear fluid film forces of a finitely long journal bearing with two axial grooves are obtained. The fluid film forces calculated by the proposed method agree well with the results obtained by the finite-difference method. The effects of the bearing parameters on the nonlinear fluid film forces are analyzed.     

Peristaltic motion of a Jeffrey fluid under the effect of a magnetic field in a tube

This study is concerned with the analysis of peristaltic motion of a Jeffrey fluid in a tube with sinusoidal wave travelling down its wall. The fluid is electrically conducting in the presence of a uniform magnetic field. Analytic solution is carried out for long wavelength and low Reynolds number considerations. The expressions for stream function, axial velocity and axial pressure gradient have been obtained. The results for pressure rise and frictional force per wavelength obtained in the analysis have been evaluated numerically and discussed briefly. The significance of the present model over the existing models has been pointed out by comparing the results with other theories. It is further noted that under the long wavelength approximation, the retardation time has no effect in the present analysis.     

二层流体中沿任意路径运动的奇点解析解*

本文求解了二层流体存在时在上层或下层流体中沿任意路径运动的奇点的速度势.流体的深度为有限或者无限.计入上层流体的影响后,流体交界面不再是等压力面或零压力面.文中给出了这种情况下的一系列奇点基本解的解析表达式.     

Peristaltic flow of a Williamson fluid in an asymmetric channel

In this work, we have presented a peristaltic flow of a Williamson model in an asymmetric channel. The governing equations of Williamson model in two dimensional peristaltic flow phenomena are constructed under long wave length and low Reynolds number approximations. A regular perturbation expansion method is used to obtain the analytical solution of the non-linear problem. The expressions for stream function, pressure gradient and pressure rise have been computed. The pertinent features of various physical parameters have been discussed graphically. It is observed that, (the non-dimensional Williamson parameter) for large We , the curves of the pressure rise are not linear but for very small We it behave like a Newtonian fluid.     

On the linearized theory op flow around bodies. Method of force sources

The method of force sources is proposed for solving linear problems related to the interaction between rigid bodies, and fluids, or gases. Method is based on the introduction of perturbation force sources into equation of motion of fluid media. Boundary conditions at the rigid body surface make it possible to reduce the problem of hydrodynamic reactions to an integral equation defining the function of force sources. Method is illustrated by the solution of three simple problems in the field of acoustics, and of viscous, and compressible media flow around bodies.

In the linearized theory of flow around rigid bodies, as well as in acoustics, an important part of the sound wave generation analysis concerns the determination of hydrodynamic reactions of the medium on moving, pulsating, or oscillating bodies. Such reactions make themselves felt as constant, or variable mechanical forces, such as drag and lift, or in the case of sound wave emitters, as the wave resistance. Various methods had been proposed for the computation of such forces, as for example, in the monographs [1 to 6].

Here, a different approach to the problem of determination of surface forces exerted by liquids and gases on the rigid body is proposed. By resorting to the formalism of the generalized functions it is possible to introduce into the equations of motion of fluid media a perturbation source in the form volume density of forces exercised by the body on the gas. The distribution of surface tension entering into the expression of this force is selected in such a manner as to satisfy boundary conditions at the body surface. It becomes possible with the use of this device to reduce the problem of determination of forces acting on the body surface to the solution of certain Integral equations. The proposed method is in all respects completely analogous to the well-known method of sources and sinks [1 to 1]. Both methods reduce the problem of interaction between body and gas to the solution of Integral equations. The method of sources and sinks, however, leads to an integral equation which describes the distribution of fictitious sources and sinks in the volume of the body having the density of the medium, while the method of force sources yields an integral equation which directly defines the distribution of mechanical forces over the surface of the body (*).

We may note that the method of force sources had to a certain extent been already used in papers [6 and 7] for the determination of sound radiation by means of point-force sources.     

On a particular form of stabilized capillary-gravitational waves of finite amplitude at the surface of fluid over an undulating bed : PMM vol. 37, n6, 1973, pp. 1020–1034

The problem of stabilized plane capillary-gravitational waves of finite amplitude at the surface of a stream of perfect incompressible fluid flowing over an undulating bed and subjected to pressure periodically distributed along the surface and defined by some infinite trigonometric series is considered. The intersection of the bed with a vertical plane is assumed to be a periodic curve, called the bed line, defined by some infinite trigonometric series. The problem is rigorously formulated and reduced to the solution of a system of nonlinear integral and transcendental equations. The solution is constructed in the form of series in powers of a small dimensionless parameter to which amplitudes of the first harmonics of the bed line and of the surface pressure wave are proportional. An approximate equation is derived for the wave profile.The particular case is considered, when the length of the bed line wave arc is equal to the length of the stabilized free wave line corresponding to the specified flow velocity over a horizontal flat bed and constant pressure along the surface. In such case the parameter of the integral equation is equal to one of the eigenvalues of the kernel of that equation and the solution is constructed in the form of series in powers of the cube root of the small parameter mentioned above.A similar problem but for constant pressure along the surface was considered by the author in [1, 2] and in his paper presented at the 13-th International Congress on Theoretical and Applied Mechanics (Moscow, 1972 [3]).Another similar problem of capillary-gravitational waves over an undulating bed was considered in [4], where besides the topological proof of the existence and uniqueness of solution the algorithm for constructing the latter is given, but the calculation of approximations is only outlined and the mechanical meaning of solution is not investigated in depth.Unlike in [4] the equation of the bed line and the expression for pressure at the surface are specified here in a form which makes it possible to express any approximations in the form of finite sums, and an analysis of the fundamental system of nonlinear integral and transcendental equations by the LiapunovSchmidt analytical methods and their developments is presented.