Fallopian tube analysis of the peristaltic-ciliary flow of third grade fluid in a finite narrow tube

The present prospective theoretical investigation deals with analysis of the peristaltic-ciliary transport of a developing embryo within the fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of viscoelastic fluid characterized by the third grade fluid model within the fallopian tubal fluid in a finite two dimensional narrow tube is developed. Non-linear partial differential equation resulting from the modelling of the proposed model is solved using perturbation method. Flow variables like axial and radial velocities, appropriate residue time over tube length, pressure difference over wavelength and stream function are analyzed for embedded parameters and constants. Salient features of the pumping characteristics and trapping phenomenon are discussed in detail. The analysis showed that embedded parameters and constants have opposite effects on axial velocity and appropriate residue time over tube length. Moreover, a comparison of the peristaltic flow with the peristaltic-ciliary flow and the third grade fluid with the linearly viscous fluid is made as a special case. The relevance of the current results to the transport of a developing embryo within the fallopian tubal fluid is also explored. It reveals that, third grade fluid instead of the linearly viscous fluid and the inclusion of cilia along with peristalsis help to complete the required mitotic divisions while transporting the developing embryo within the fallopian tubal fluid in the human fallopian tube.     

Peristaltically induced transport of a MHD biviscosity fluid in a non-uniform tube

We have analyzed an incompressible flow of electrically conducting biviscosity fluid through an axisymmetric non-uniform tube with a sinusoidal wave under the considerations of long wavelength and low Reynolds number. In our analysis we are taking into account the induced magnetic field. The analytic solution has been obtained from which the axial velocity, the axial induced magnetic field and the axial pressure gradient have been derived. The results for the pressure rise ΔP_λ(t), frictional force per wavelength F_λ(t) and the axial induced magnetic field h_z have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the magnetic Prandtl number p_m, the magnetic field parameter M, the Reynolds number Re, the upper limit apparent viscosity coefficient β, and the time averaged mean flow rate θ.     

Peristaltic blood flow with gold nanoparticles as a third grade nanofluid in catheter: Application of cancer therapy

Cancer is dangerous and deadly to most of its patients. Recent studies have shown that gold nanoparticles can cure and overcome it, because these particles have a high atomic number which produce the heat and leads to treatment of malignancy tumors. A motivation of this article is to study the effect of heat transfer with the blood flow (non-Newtonian model) containing gold nanoparticles in a gap between two coaxial tubes, the outer tube has a sinusoidal wave traveling down its wall and the inner tube is rigid. The governing equations of third-grade fluid along with total mass, thermal energy and nanoparticles are simplified by using the assumption of long wavelength. Exact solutions have been evaluated for temperature distribution and nanoparticles concentration, while approximate analytical solutions are found for the velocity distribution using the regular perturbation method with a small third grade parameter. Influence of the physical parameters such as third grade parameter, Brownian motion parameter and thermophoresis parameter on the velocity profile, temperature distribution and nanoparticles concentration are considered. The results pointed to that the gold nanoparticles are effective for drug carrying and drug delivery systems because they control the velocity through the Brownian motion parameter $N_b$ and thermophoresis parameter $N_t$. Gold nanoparticles also increases the temperature distribution, making it able to destroy cancer cells.     

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.     

Existence of a Hartmann layer in the peristalsis of Sisko fluid

Analytical solutions for the peristaltic flow of a magneto hydrodynamic(MHD) Sisko fluid in a channel, under the effects of strong and weak magnetic fields, are presented. The governing nonlinear problem, for the strong magnetic field,is solved using the matched asymptotic expansion. The solution for the weak magnetic field is obtained using a regular perturbation method. The main observation is the existence of a Hartman boundary layer for the strong magnetic field at the location of the two plates of the channel. The thickness of the Hartmann boundary layer is determined analytically. The effects of a strong magnetic field and the shear thinning parameter of the Sisko fluid on the velocity profile are presented graphically.     

Studying effect of MHD on thin films of a micropolar fluid

This paper deals with the study of the effect of MHD on thin films of a micropolar fluid. These thin films are considered for three different geometries, namely: (i) flow down an inclined plane, (ii) flow on a moving belt and (iii) flow down a vertical cylinder. The transformed boundary layer governing equations of a micropolar fluid and the resulting system of coupled non-linear ordinary differential equations are solved numerically by using shooting method. Numerical results were presented for velocity and micro-rotation profiles within the boundary layer for different parameters of the problem including micropolar fluid parameters, magnetic field parameter, etc., which are also discussed numerically and illustrated graphically.     

Peristaltic flow of a couple stress fluid in an annulus: Application of an endoscope

This paper discusses the influence of an endoscope on the peristaltic flow of a couple stress fluid in an 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. Analytical expressions for the axial velocity, stream function and axial pressure gradient are established. The flow is investigated in a wave frame of reference moving with the velocity of the wave. Numerical calculations are carried out for the pressure rise, frictional forces and trapping. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail.     

A new numerical solution for the MHD peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube via Adomian decomposition method

In this Letter, we considered a numerical treatment for the solution of the hydromagnetic peristaltic flow of a bio-fluid with variable viscosity in a circular cylindrical tube using Adomian decomposition method and a modified form of this method. The axial velocity is obtained in a closed form. Comparison is made between the results obtained by only three terms of Adomian series with those obtained previously by perturbation technique. It is observed that only few terms of the series expansion are required to obtain the numerical solution with good accuracy.     

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.     

Hall effect on Hartmann flow and heat transfer of a Burgers' fluid

The effect of Hall current on the steady magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers' fluid between two parallel electrically insulating infinite planes is studied. The MHD flow is generated by applying constant pressure gradient. An external uniform magnetic field normal to the disks is applied. The disks are kept at two different constant temperatures. Exact solutions are obtained for the governing momentum and energy equations. The effects of Hartmann number M, Reynolds number Re, Prandtl number Pr, Eckert number Ec, pressure gradient dp/dx and Hall parameter η are examined.     

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.     

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.     

Biomagnetic fluid flow in a channel with stenosis

In this study, the fundamental problem of the biomagnetic (blood) fluid flow in a channel with stenosis under the influence of a steady localized magnetic field is studied. The mathematical model used for the formulation of the problem is consistent with the principles of ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD). Blood is considered as a homogeneous Newtonian fluid and is treated as an electrically conducting magnetic fluid which also exhibits magnetization. For the numerical solution of the problem, which is described by a coupled, non-linear system of PDEs, with appropriate boundary conditions, the stream function-vorticity formulation is adopted. The solution is obtained by the development of an efficient pseudotransient numerical methodology using finite differences. This methodology is based on the development of a semi-implicit numerical technique, transformations and stretching of the grid and proper construction of the boundary conditions for the vorticity. Results concerning the velocity and temperature field, skin friction and rate of heat transfer indicate that the presence of the magnetic field influences the flow field considerably.     

MHD from a Microscopic Concept and Onset of Turbulence in Hartmann Flow

We derive higher order magneto-hydrodynamic （MHD） equations from a microscopic picture using pro-jection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards the center at the onset of turbulence in hydrodynamic limit. Comparison with the system under the effect of a uniform magnetic field yields difference in the onset of turbulence consistent with observations, showing that the presence of magnetic field inhibits onset of instability or turbulence. The laminar-turbulent transition is demonstrated in a phase transition plot of the development in time of the relative average velocities vs. Reynolds number showing a sharp increase of the relative average velocity at the transition point as determined by the critical Reynolds number.     

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.     

Thermal radiation effects on MHD flow of a micropolar fluid over a stretching surface with variable thermal conductivity

In this paper, the effects of variable thermal conductivity and radiation on the flow and heat transfer of an electrically conducting micropolar fluid over a continuously stretching surface with varying temperature in the presence of a magnetic field are considered. The surface temperature is assumed to vary as a power-law temperature. The governing conservation equations of mass, momentum, angular momentum and energy are converted into a system of non-linear ordinary differential equations by means of similarity transformation. The resulting system of coupled non-linear ordinary differential equations is solved numerically. The numerical results show that the thermal boundary thickness increases as the thermal conductivity parameter S$S$ increases, while it decreases as the radiation parameter F$F$ increases. Also, it was found that the Nusselt number increases as F$F$ increases and decreases as S$S$ increases.     

Oscillatory limited compressible fluid flow induced by the radial motion of a thick-walled piezoelectric tube

A simple oscillatory, slightly compressible, fluid flow model in a thick-walled piezoelectric tube used in a drop-on-demand inkjet print head is developed from the point of view of fluid-structure interaction to take account of pressure wave propagation and pressure loading opposing wall motion. A frequency sweep is performed computationally using the model revealing the first acoustic fluid-structure resonance frequency and the influence of fluid viscosity. The validity of the model, with given information on the speed of sound in a fluid, is evaluated by comparing the theoretically predicted resonance frequency to the experimentally measured resonance frequency. In addition, the intrinsic speed of sound can be easily computed using the measured acoustic resonance frequency and this computed speed of sound agrees closely with speeds of sound reported in the literature.     

Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface

This Letter looks at the rotating flow of a second grade fluid past a porous shrinking surface. The fluid is electrically conducting in the presence of a constant applied magnetic field. The governing partial differential equations are first reduced into ordinary differential equations and then solved by homotopy analysis method (HAM). Convergence of the series solution is shown explicitly. In addition, the obtained results are illustrated graphically to indicate the effects of the pertinent physical parameters.     

基于MHD的磁射流抛光中流场的分析与模拟

从理论上分析了磁射流抛光中的磁场与流场的相互作用,构建了磁射流抛光的冲击射流模型,基于磁流体动力学对磁射流抛光过程的紊动冲击射流进行数值模拟,得到了磁射流抛光过程的连续流场和射流在工件壁面上的压力、速度、紊动强度分布。通过比较射流抛光和磁射流抛光的数值计算结果,分析了磁流变效应对射流稳定性的影响,从射流的流场、速度、紊动强度等方面分析射流在磁场中稳定的原因。     

Experimental study of heat transfer characteristics in oscillating fluid flow in tube

In the present work, an experimental investigation of heat transfer enhancement parameters of the oscillating flow heat exchanger under different frequencies, tidal displacement, and heat fluxes is carried out. The effect of different parameters on experimental effective thermal conductivity and convective heat transfer coefficient in cooling region is studied using correlations given by different researchers. A correlation for experimental effective thermal conductivity in terms of S²√ω is derived based on experimental data. This correlation is useful for predicting the optimum value of S²√ω before onset of turbulence.