95 research outputs found

    Peristaltic motion of Carreau fluid in a channel with convective boundary conditions

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    Abstract. We investigate the peristaltic motion of Carreau fluid in an asymmetric channel with convective boundary conditions. Mathematical formulation is first reduced in a wave frame of reference and then solutions are constructed by long wavelength and low Reynolds number conventions. Results of the stream function, axial pressure gradient, temperature and pressure rise over a wavelength are obtained for small Weissenberg number. Velocity and temperature distributions are analyzed for different parameters of interest. A comparative study between the results of Newtonian and Carreau fluids is given

    PERISTALTIC FLOW OF LITHOGENIC BILE IN THE VATERI'S PAPILLA AS NON-NEWTONIAN FLUID IN THE FINITE-LENGTH TUBE: ANALYTICAL AND NUMERICAL RESULTS FOR REFLUX STUDY AND OPTIMIZATION

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    Bile is one of 32 bio-fluids in the human body. Lithogenic bile (bile with tendency for the gallstones formation) is the pathological state of bile. Rheological properties of lithogenic bile differ from normal one. The Vateri's papilla is the narrowest duct in the biliary system. Peristaltic motion plays important role in the bile flow in the Vateri's papilla. In the literature, there are many papers devoted to peristaltic flow of fluids in the infinite length tubes. There are not many papers devoted to peristaltic flow of fluids in the finite length tubes. Modelling of peristaltic flow in the finite length tubes requires the imposing of boundary conditions on the ends of a tube. It leads to problem statement complication and to obtain the problem solution is getting harder. The current paper aims at developing mathematical model of the peristaltic bile transport flow through the duct at papillary stenosis as a tapered finite-length tube. It allows evaluating velocities and pressure distribution along the tube, and detecting choledochopancreatic reflux occurrence conditions. Adopting the perturbation method, the analytical solutions for velocities and pressures are obtained. Pressure distribution versus axial coordinate at different time instants are plotted for various values of Weissenberg number and amplitude ratio. It revealed that the amplitude ratio has more effect on the pressure distribution along the tube compared to the Weissenberg number. The values of the pressure gradient corresponding to reflux occurring are obtained. The comparison between developed model and numerical peristaltic model code implemented in ANSYS was made. Moreover, it is reported that the pressure drop value corresponding to average flow rate equal to zero may serve as reflux occurrence criterion. Moreover, channel shape optimization was made for subsequent stent installation to restore normal bile flow using Nelder-Mead method

    Electro-Osmotic Flow of MHD Jeffrey Fluid in a Rotating Microchannel by Peristalsis: Thermal Analysis

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    In this study, we examine the rotating and heat transfer on the peristaltic and electro-osmatic flow of a Jeffery fluid in an asymmetric microchannel with slip impact. A pressure gradient and anal axially imposed electric field work together to impact the electro-osmotic flow (EOF). Mathematical modeling is imported by employing the low Reynolds number and long wavelength approximation. The exact solution has been simplified for the stream function, temperature, and velocity distributions. The effects of diverse egress quantities on the gush virtue are exhibited and discussed with the help of graphs. The shear stress and trapping phenomena have been investigated. The characterization of results has been resolved for the flow governing ingrained appropriate parameters by employing the table. Our findings can be summarized as follows: (i) Debye length has a strong influence on the conducting viscous fluid of EOF in non-uniform micro-channel. (ii) The temperature field is enhanced through the elevated values of the rotation parameter and EOF. (iii) The shear stress has oscillatory behavior and the heat transmission rate increases with the magnitude of larger values of EOF. Finally, there is good agreement between the current results and those that have already been published. This model applies to the study of chemical fraternization/separation procedures and bio-microfluidic devices for the resolution of diagnosis

    Electro-Osmotic Blood Flow of Shear-Thinning Fluid with Hall Current and Wall Flexibility

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    The presented article aims to present the flow of blood in microchannels such as veins and arteries via peristaltic flow.  The magnetic field is imposed to regulate the flow as laminar. Also, its impacts in terms of Hall current have been considered. The rate of heat transfer is further based on Joule heating and viscous dissipation aspects. Mathematical analysis has been conducted given long wavelength and small Reynolds number. Such preferences are relatable to the medical domain where the magnetic field regulates the flow stream and aids in the melting of blood clots in patients with various heart diseases. The solution for electric potential is calculated analytically while the velocity, temperature, and heat transfer rate are executed directly via the built-in command of Mathematica software. Since the magnetic field acts as an opposing force. Results show that the velocity and temperature are decreasing functions of the magnetic field. However, the temperature is increasing for Weissenberg number

    Effects of MHD and wall properties on the peristaltic transport of a Carreau fluid through porous medium

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    This work concerns the peristaltic flow of a Carreau fluid model through porous medium under combined effects of MHD and wall properties. The assumptions of Reynolds number and long wavelength is investigated. The flow is investigated in a wave frame of reference moving with velocity of the wave. The perturbation series in terms of the Weissenberg number (We <1) was used to obtain explicit forms for velocity field and stream function. The effects of thermal conductivity, Grashof number, Darcy number, magnet, rigidity, stiffness of the wall and viscous damping force parameters on velocity, temperature and stream function have been studied

    Effects of Bivariation Viscosity and Magnetic Field on Trapping in a Uniform Tube with Peristalsis

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    In recent papers, Mehdi Lachiheb has considered fluid viscosity through a peristaltic tube and a channel as a function of the radial and axial components. This author discussed the trapping phenomenon at the centerline of a peristaltic tube and a channel, the pressure rise, and the drag (friction) forces without a magnetic field. Considering the importance of magnetohydrodynamic fluids in bioengineering and medical sciences, we discussed the effects of bivariation viscosity and magnetic field on the trapping phenomenon at the centerline, separated flow on the wall surface of the peristaltic tube, the drag (friction) forces, and the pressure rise. To solve the problem under low Reynolds and long wavelength assumptions, the velocity field and pressure gradient as functions of Hartmann number, amplitude ratio, viscosity parameter, and volume flow rate were obtained using the perturbation approach in terms of Hartmann number (M \u3c 1). The peristaltic pumping and augmented pumping regions were discussed through drag (friction) forces and the pressure rising. In addition, separation flow points on the surface of the wall were determined numerically

    MHD Peristaltic Flow of a Couple Stress Fluids with Heat and Mass Transfer through a Porous Medium

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    In the present article, we have studied the effects of heat and mass transfer on the MHD flow of an incompressible, electrically conducting couple stress fluid through a porous medium in an asymmetric flexible channel over which a traveling wave of contraction and expansion is produced, resulting in a peristaltic motion. The flow is examined in a wave frame of reference moving with the velocity of the wave. Formulas of dimensionless velocity, temperature and concentration are obtained analytically under assumptions of long wavelength and low Reynolds number. The effects of various parameters of interest such as the couple stress fluid parameter, Darcy number, Hartmann number and Schmidt number on these formulas were discussed and illustrated graphically through a set of figures. Key words: peristalsis,  Couple stress fluid,  Porous medium,  MHD flow, Heat transfer,  Mass transfer

    Effect of Inclined Magnetic Field on Peristaltic Flow of Carreau Fluid through Porous Medium in an Inclined Tapered Asymmetric Channel

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    During this article, we have a tendency to show the peristaltic activity of magnetohydrodynamics flow of carreau fluid with heat transfer influence in an inclined tapered asymmetric channel through porous medium by exploitation the influence of non-slip boundary conditions. The tapered asymmetric channel is often created because of the intrauterine fluid flow induced by myometrial contraction and it had been simulated by asymmetric peristaltic fluid flow in an exceedingly two dimensional infinite non uniform channel, this fluid is known as hereby carreau fluid, conjointly we are able to say that one amongst carreau's applications is that the blood flow within the body of human. Industrial field, silicon oil is an example of carreau fluid. By exploitation, the perturbation technique for little values of weissenberg number, the nonlinear governing equations in the two-dimensional Cartesian coordinate system is resolved under the assumptions of long wavelength and low Reynolds number. The expressions of stream function, temperature distribution, the coefficient of heat transfer, frictional forces at the walls of the channel, pressure gradient are calculated. The effectiveness of interesting parameters on the inflow has been colluded and studied

    The study of non-Newtonian nanofluid with hall and ion slip effects on peristaltically induced motion in a non-uniform channel

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    In this study, we considered the unsteady peristaltic motion of a non-Newtonian nanofluid under the influence of a magnetic field and Hall currents. The simultaneous effects of ion slip and chemical reaction were also taken into consideration. The flow problem was suggested on the basis of the continuity, thermal energy, linear momentum, and nanoparticle concentration, which were further reduced with the help of Ohm's law. Mathematical modelling was executed using the lubrication approach. The resulting highly nonlinear partial differential equations were solved semi-analytically using the homotopy perturbation technique. The impacts of all the pertinent parameters were investigated mathematically and graphically. Numerical calculations have been used to calculate the expressions for the pressure increase and friction forces along the whole length of the channel. The results depict that for a relatively large value of the Brownian parameter, the chemical reaction has a dual behaviour on the concentration profile. Moreover, there is a critical point of the magnetic parameter at which the behaviours of the pressure increase and friction forces are reversed for progressive values of the power law index. The present investigation provides a theoretical model that estimates the impact of a wide range of parameters on the characteristics of blood-like fluid flows

    Unsteady 3D MHD Carreau and Casson Fluids over a Stretching Sheet with Non-Uniform Heat Source/Sink

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    In this study, we analyzed the effects of nonlinear thermal radiation and non-uniform heat source/sink on an unsteady three-dimensional flow of Carreau and Casson fluid past a stretching surface. The transformed governing equations are solved numerically using Runge-Kutta based shooting technique. We obtained better accuracy of the present results by comparing with the already published literature. The influence of dimensionless parameters on velocity and temperature profiles along with the friction factors, local Nusselt and Sherwood numbers are discussed with the help of graphs and tables. We presented dual nature solutions for the flow over a Carreau and Casson fluid cases. It is also found that the non-uniform heat source or sink is control the thermal boundary layer for both the Casson and Carreau fluid cases. Keywords: MHD, unsteady, nonlinear thermal radiation, Carreau fluid, Casson fluid, 3D
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