Showing papers on "Stream function published in 2015"
TL;DR: In this article, a model of wall-induced fluid flow within an infinite tapered channel has been developed to simulate the transport phenomena due to asymmetric wall displacements, and the analytical solution has been obtained for the temperature and concentration of the nanofluid.
142 citations
TL;DR: In this paper, the least square method (LSM) was used to solve the problem of micropolar fluid flow in a channel subject to a chemical reaction and the results reveal that the LSM can achieve suitable results in predicting the solution of these problems.
132 citations
TL;DR: In this paper, the influence of magnetic field on peristaltic flow of a Casson fluid model is considered, and the model is modelled first time under long wavelength and low Reynold's number approximation.
113 citations
TL;DR: In this article, the effect of radiation and MHD on peristaltic flow of a nanofluid through a porous medium in a two dimensional tapered asymmetric channel has been made.
101 citations
TL;DR: In this paper, the impact of applied magnetic field on peristaltic transport of Carreau-Yasuda fluid in a curved conduit is analyzed and Hall effects are also taken into consideration.
88 citations
TL;DR: In this paper, the effects of Brownian motion and thermophoretic diffusion of nanoparticles in a channel with complaint walls were investigated and closed form solution for stream function was computed and resulting coupled nonlinear equations were solved numerically by using shooting technique through computational software Mathematica.
78 citations
TL;DR: In this paper, the effects of magnetic field and heat transfer on the peristaltic flow of an incompressible couple stress fluid through porous medium in an inclined asymmetric channel have been studied under the long wavelength approximation.
73 citations
TL;DR: In this article, the authors investigated the natural convection flow in a porous concentric horizontal annulus saturated with a water-based nanofluid and showed that inclusion of nanoparticles into pure water changes the flow structure at low values of the Rayleigh number.
54 citations
TL;DR: It is shown that the flow rate always decreases due to the wall corrugations irrespective of the phase difference, and the obtained results for the flow rates as a function of the applied current are in qualitative agreement with the existing experimental results.
Abstract: In this paper, 2D electromagnetohydrodynamic (EMHD) flow in a microparallel channel with slightly transverse corrugated walls is investigated using perturbation method. The corrugations of the two walls are presented by periodic sinusoidal waves with small amplitudes. The perturbation solutions of the stream function and a relation between flow rate and roughness are obtained. It is shown that the flow rate always decreases due to the wall corrugations irrespective of the phase difference. For prescribed Hartmann number and wave number of the wavy walls, the flow resistance increases as the phase difference between the wall corrugations increases. The effect of corrugation on the flow rate decreases with Hartmann number. With the increase of wave number, the effects of corrugations on the flow rate increase. The phase difference of wall corrugations becomes unimportant when the wave number is greater than 4. The obtained results for the flow rates as a function of the applied current are in qualitative agreement with the existing experimental results.
53 citations
TL;DR: In this article, a particle-fluid suspension model for axi-symmetric flow of blood through curved coaxial tubes where the outer tube with mild overlapping stenosis is uniform rigid representing catheter is formulated using a perturbation expansion in terms of a variant of curvature parameter.
48 citations
TL;DR: In this paper, the authors present transient turbulent natural convection with surface thermal radiation in a square differentially heated enclosure using non-primitive variables like stream function and vorticity.
Abstract: Purpose – The purpose of this paper is to present transient turbulent natural convection with surface thermal radiation in a square differentially heated enclosure using non-primitive variables like stream function and vorticity. Design/methodology/approach – The governing equations formulated in dimensionless variables “stream function, vorticity and temperature,” within the Boussinesq approach taking into account the standard two equation k-e turbulence model with physical boundary conditions have been solved using an iterative implicit finite-difference method. Findings – It has been found that using of the presented algebraic transformation of the mesh allows to effectively conduct numerical analysis of turbulent natural convection with thermal surface radiation. It has been shown that the average convective Nusselt number increases with the Rayleigh number and decreases with the surface emissivity, while the average radiative Nusselt number is an increasing function of these key parameters. It has be...
27 Jul 2015
TL;DR: A stream function approach to liquid simulations with novel boundary conditions for free surfaces, solid obstacles, and solid-fluid coupling, which increases the dimension of the linear system necessary to enforce incompressibility and provides interesting and surprising benefits.
Abstract: This paper presents a liquid simulation technique that enforces the incompressibility condition using a stream function solve instead of a pressure projection. Previous methods have used stream function techniques for the simulation of detailed single-phase flows, but a formulation for liquid simulation has proved elusive in part due to the free surface boundary conditions. In this paper, we introduce a stream function approach to liquid simulations with novel boundary conditions for free surfaces, solid obstacles, and solid-fluid coupling. Although our approach increases the dimension of the linear system necessary to enforce incompressibility, it provides interesting and surprising benefits. First, the resulting flow is guaranteed to be divergence-free regardless of the accuracy of the solve. Second, our free-surface boundary conditions guarantee divergence-free motion even in the un-simulated air phase, which enables two-phase flow simulation by only computing a single phase. We implemented this method using a variant of FLIP simulation which only samples particles within a narrow band of the liquid surface, and we illustrate the effectiveness of our method for detailed two-phase flow simulations with complex boundaries, detailed bubble interactions, and two-way solid-fluid coupling.
TL;DR: In this article, a pressure driven peristaltic flow of nanofluid in a curved channel is investigated, where the flow exploration demeanors the induced magnetic field.
TL;DR: In this article, a new stream function/log-conformation formulation of incompressible viscoelastic flows is presented, which guarantees the positive-definiteness of the conformation tensor and obviates the high Weissenberg number problem.
Abstract: A new streamfunction/log-conformation formulation of incompressible viscoelastic flows is presented. The log-conformation representation guaranties the positive-definiteness of the conformation tensor and obviates the high Weissenberg number problem. The streamfunction is defined as a vector potential of the velocity field, and provides a pressureless formulation of the conservation laws, which automatically enforces the incompressibility. The resulting numerical method is free from velocity–pressure decoupling errors, and can achieve stable calculations for large Courant numbers, which improve the robustness and the efficiency of the solver. The two-dimensional flow of an Oldroyd-B fluid inside the lid-driven cavity is simulated for a large range of Weissenberg numbers. The numerical results demonstrate the second-order accuracy of our scheme, and our solutions are in good agreement with the available data from the literature for Weissenberg number 3 and below. Finally, the simulations at higher Weissenberg numbers 5 and 10 reveal a structural mechanism that sustains quasi-periodic elastic instabilities arising at the upstream corner of the moving lid.
TL;DR: In this article, the influence of magnetic field for metachoronical beating of cilia for nanofluid with Newtonian heating in an asymmetric channel is considered.
TL;DR: In this paper, an analysis of the peristaltic pumping of a non-Newtonian Ellis fluid in a planar channel was carried out, and the coupled nonlinear partial differential equations governing the problem were simplified under the widely used assumption of long wavelength and low Reynolds number.
Abstract: An analysis is carried out to investigate the peristaltic pumping of a non-Newtonian Ellis fluid in a planar channel. The coupled nonlinear partial differential equations governing the problem are simplified under the widely used assumption of long wavelength and low Reynolds number. A semi- analytical approach is adopted to obtain the expressions for stream function, longitudinal velocity, pressure gradient and pressure rise per wavelength. The important characteristics of the peristaltic motion are explained graphically for several values of the material parameter of the Ellis fluid.
09 Mar 2015
TL;DR: In this paper, the effects of heat and mass transfer on the peristaltic transport of magnetohydrodynamic couple stress fluid through homogeneous porous medium in a vertical asymmetric channel were investigated.
Abstract: The intrauterine fluid flow due to myometrial contractions is peristaltic type motion and the myometrial
contractions may occur in both symmetric and asymmetric directions. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitude, and phase due to the variation of channel width, wave amplitudes and phase differences. In this paper, we study the effects of heat and mass transfer on the peristaltic transport of magnetohydrodynamic couple stress fluid through homogeneous porous medium in a vertical asymmetric channel. The flow is investigated in the wave frame of reference moving with constant velocity with the wave. The governing equations of couple stress fluid have been simplified under the long wave length approximation. The exact solutions of the resultant governing equations have been derived for the stream function, temperature, concentration, pressure gradient, and heat transfer coefficients. The pressure difference and frictional forces at both the walls are calculated using numerical integration. The influence of diverse flow parameters on the fluid velocity, pressure gradient, temperature, concentration, pressure difference, frictional forces, heat transfer coefficients, and trapping has been discussed. The graphical results are also discussed for four different wave shapes. It is noticed that increasing of couple
stresses and heat generation parameter increases the size of the trapped bolus. The heat generation parameter increases the peristaltic pumping and temperature.
TL;DR: In this paper, a benchmark solution for the conjugate heat transfer of backward-facing step flow is computed using the stream function vorticity formulation using the multidomain Boundary Element Method.
TL;DR: In this study, two dimensional flow of a viscous fluid in the presence of nanoparticles are observed in a curved channel with ciliated walls and the mechanism of cilia-induced flow is discussed through a mathematical model.
Abstract: In this paper, the mechanism of cilia-induced flow is discussed through a mathematical model. In this study two dimensional flow of a viscous fluid in the presence of nanoparticles are observed in a curved channel with ciliated walls. Cilia have a distinctive pattern of motion by which they can set fluid into motion at low Reynolds number. The flow is modeled in both fixed and wave frame of reference. Exact solution is calculated for the velocity as well as for temperature profile and the flow properties for the Cu-blood nanofluid is determined as a function of the cilia and metachronal wave velocity. Results for temperature profile, velocity, pressure rise, pressure gradient and stream function are constructed and evaluated graphically.
TL;DR: In this article, a numerical investigation is performed on the unsteady natural convection with a temperature-dependent viscosity inside a square porous cavity, where the vertical walls of the cavity are kept at constant but different temperatures, while the horizontal walls are adiabatic.
Abstract: A numerical investigation is implemented on the unsteady natural convection with a temperature-dependent viscosity inside a square porous cavity. The vertical walls of the cavity are kept at constant but different temperatures, while the horizontal walls are adiabatic. The mathematical model formulated in dimensionless stream function, vorticity and temperature variables is solved using implicit finite difference schemes of the second order. The governing parameters are the Rayleigh number, Darcy number, viscosity variation parameter and dimensionless time. The effects of these parameters on the average Nusselt number along the hot wall as well as on the streamlines and isotherms are analyzed. The results show an intensification of convective flow and heat transfer with an increase in the viscosity variation parameter for the porous media, while in the case of pure fluid, the effect is opposite.
TL;DR: In this paper, the effects of pertinent parameters involved in the problem, namely, magnetic parameter, Prandtl number, and impinging angle, on flow and heat transfer characteristics are illustrated.
Abstract: Unsteady stagnation point flow impinging obliquely on an oscillating flat plate in the presence of a uniform applied magnetic field in a fixed frame has been studied. The governing boundary layer equations are transformed into three coupled, dimensionless, nonlinear, partial differential equations. Here the stream function is expressed as Hiemenz and tangential components. The equations are solved numerically by using the well-known implicit finite difference scheme, called the Keller-box method. To ensure the accuracy of obtained results, numerical results are compared with the results available in the literature. It is observed that the obtained solution is in excellent agreement with previous studies. The effects of pertinent parameters involved in the problem, namely, magnetic parameter, Prandtl number, and impinging angle, on flow and heat transfer characteristics are illustrated. It is observed that the magnetic field helps to translate the oblique stagnation point.
TL;DR: The effects of heat transfer on peristaltic flow of carbon nanoparticles in a curved channel is investigated by analysing the effects of curvature of the curved channel and taking inboard the long wavelength and small Reynolds number assumptions.
TL;DR: In this article, the peristaltic flow and heat transfer through a symmetric channel in the presence of heat sink/source parameter have been analyzed in terms of temperature, velocity, stream function, pressure rise and frictional forces.
Abstract: The peristaltic flow and heat transfer through a symmetric channel in the presence of heat sink/source parameter have been analyzed in this paper. It also deals with the effect of the natural convection coefficient in the momentum equation. Low Reynolds number and small wave number approximation are used to convert the non-linear partial differential equations into the non-linear ordinary differential equations. In order to solve the governing model, perturbation method has been chosen by taking α (material parameter) as a small parameter. Expressions have been obtained for temperature, velocity, stream function, pressure rise and frictional forces. The features of the flow characteristics are analyzed by plotting graphs and the results are discussed in details. It has been observed that velocity increases with an increase of α (material parameter). The peristaltic pumping and in the copumping region the pumping rate decreases by increasing the value of α (material parameter). The size of the trapped bolus decreases by increasing the value of α (material parameter). The temperature profile increases by increasing the value of β 1 (heat sink/source parameter).
TL;DR: The present model is applicable to study the behavior of intestinal flow (chyme movement from small intestine to large intestine), and is also relevant to simulations of biomimetic pumps conveying hazardous materials, polymers, and so forth.
Abstract: A mathematical study on creeping flow of non-Newtonian fluids (power law model) through a nonuniform peristaltic channel, in which amplitude is varying across axial displacement, is presented, with slip effects included. The governing equations are simplified by employing the long wavelength and low Reynolds number approximations. The expressions for axial velocity, stream function, pressure gradient, and pressure difference are obtained. Computational and numerical results for velocity profile, pressure gradient, and trapping under the effects of slip parameter, fluid behavior index, angle between the walls, and wave number are discussed with the help of Mathematica graphs. The present model is applicable to study the behavior of intestinal flow (chyme movement from small intestine to large intestine). It is also relevant to simulations of biomimetic pumps conveying hazardous materials, polymers, and so forth.
TL;DR: In this article, an axisymmetric upper bound method was proposed to analyze the inhomogeneity of axial metal flow in the radial forging process from the viewpoint of end profile in the meridian plane of the workpiece.
TL;DR: In this article, the influence of inclined magnetic field, heat source, thermal radiation, and chemical reactions on peristaltic flow of a Newtonian nanofluid in a vertical generalized (tapered asymmetric) channel was studied.
Abstract: In this paper, we study the influences of inclined magnetic field, heat source, thermal radiation, and chemical reactions on peristaltic flow of a Newtonian nanofluid in a vertical generalized (tapered asymmetric) channel. The flow is engendered because of an asymmetric sinusoidal wave on the non-uniform channel walls. The Rosseland approximation is viewed in the modeling of the conduction radiation heat transfer, and temperatures of the walls are presumed constants. The governing equations are uttered in a non-dimensional form, and the series solutions of coupled system of equations are constructed for temperature and nanoparticle concentration using a homotopy perturbation method. Analytical solutions have been developed for stream function and axial velocity. Numerical integrations have been applied to receive the graphical results for an average rise in pressure. The variations of various interesting dimensionless parameters are sketched and discussed. It is observed that the temperature profile increases with an increase of the non-uniform parameter, while it decreases when the thermal radiation parameter is increased. © 2015 Curtin University of Technology and John Wiley & Sons, Ltd.
TL;DR: In this paper, the effect of permeable walls and magnetic field on peristaltic flow of a Carreau fluid in a tapered asymmetric channel is studied and the results have been presented graphically for the various interested physical parameters.
Abstract: The effect of permeable walls and magnetic field on the peristaltic flow of a Carreau fluid in a tapered asymmetric channel is studied. The tapered asymmetric channel is normally created due to the intra-uterine fluid flow induced by myometrial contractions and it was simulated by asymmetric peristaltic fluid flow in a two-dimensional infinite non-uniform channel. The analysis has been performed under long wavelength and low-Reynolds number assumptions to linearize the governing flow equations. A series solution in respect of a small Weissenberg number is obtained for the stream function, axial pressure gradient and shear stress. Time average of pressure rise and frictional force on the upper wall has also been computed using numerical integration. The results have been presented graphically for the various interested physical parameters. It is observed that for Carreau fluids the peristalsis works as a pump against a greater pressure rise compared with a Newtonian fluid, while there exists no significant...
TL;DR: In this paper, an analytical study of electro-osmotic flow in a Hele-Shaw configuration with non-uniform zeta potential distribution is presented, where the authors obtain a pair of uncoupled Poisson equations for the pressure and depth-averaged stream function, and show that the inhomogeneous parts in these equations are governed by gradients in Zeta potential parallel and perpendicular to the applied electric field.
Abstract: We present an analytical study of electro-osmotic flow in a Hele-Shaw configuration with non-uniform zeta potential distribution. Applying the lubrication approximation and assuming thin electric double layer, we obtain a pair of uncoupled Poisson equations for the pressure and depth-averaged stream function, and show that the inhomogeneous parts in these equations are governed by gradients in zeta potential parallel and perpendicular to the applied electric field, respectively. We obtain a solution for the case of a disk-shaped region with uniform zeta potential and show that the flow field created is an exact dipole, even in the immediate vicinity of the disk. In addition, we study the inverse problem where the desired flow field is known and solve for the zeta potential distribution required in order to establish it. Finally, we demonstrate that such inverse problem solutions can be used to create directional flows confined within narrow regions, without physical walls. Such solutions are equivalent to flow within channels and we show that these can be assembled to create complex microfluidic networks, composed of intersecting channels and turns, which are basic building blocks in microfluidic devices.
TL;DR: A mathematical model is developed to study the transport mechanism of a Casson fluid flow inspired by the metachronal coordination between the beating cilia in a cylindrical tube and it is observed that the volume flow rate is influenced significantly by the width of plug flow region H p as well as the cilia length parameter ε.
Abstract: A mathematical model is developed to study the transport mechanism of a Casson fluid flow inspired by the metachronal coordination between the beating cilia in a cylindrical tube. A two-dimensional system of nonlinear equations governing the flow problem is formulated by using axisymmetric cylindrical coordinates and then simplified by employing the long wavelength and low Reynolds number assumptions. Exact solutions are derived for the velocity components, the axial pressure gradient, and the stream function. However, the expressions for the pressure rise and the volume flow rate are evaluated numerically. The features of the flow characteristics such as pumping and trapping are illustrated and discussed with the help of graphs. It is observed that the volume flow rate is influenced significantly by the width of plug flow region H p as well as the cilia length parameter e. The analysis is also applied and compared with the estimated value of the volume flow rate of epididymal fluid in the ductus efferentes of the human male reproductive tract.
TL;DR: In this article, the effects of wall slip conditions, elasticity wall properties and heat transfer on the peristaltic transport of conducting Bingham fluid in a non-uniform channel under the assumptions of long wavelength and low Reynolds number are investigated.