Showing papers on "Stream function published in 2014"

A Stream Virtual Element Formulation of the Stokes Problem on Polygonal Meshes

Abstract: In this paper we propose and analyze a novel stream formulation of the virtual element method (VEM) for the solution of the Stokes problem. The new formulation hinges upon the introduction of a suitable stream function space (characterizing the divergence free subspace of discrete velocities) and it is equivalent to the velocity-pressure (inf-sup stable) mimetic scheme presented in [L. Beirao da Veiga et al., J. Comput. Phys., 228 (2009), pp. 7215--7232] (up to a suitable reformulation into the VEM framework). Both schemes are thus stable and linearly convergent but the new method results to be more desirable as it employs much less degrees of freedom and it is based on a positive definite algebraic problem. Several numerical experiments assess the convergence properties of the new method and show its computational advantages with respect to the mimetic one.

Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration

Abstract: In this article we derive semi-analytical/numerical solutions for transport phenomena (momentum, heat and mass transfer) in a nanofluid regime adjacent to a nonlinearly porous stretching sheet by means of the Homotopy analysis method (HAM). The governing equations are reduced to a nonlinear, coupled, non-similar, ordinary differential equation system via appropriate similarity transformations. This system is solved under physically realistic boundary conditions to compute stream function, velocity, temperature and concentration function distributions. The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation. Furthermore the current HAM solutions demonstrate very good correlation with the non-transpiring finite element solutions of Rana and Bhargava (Commun. Nonlinear Sci. Numer. Simul. 17:212–226, 2012). The influence of stretching parameter, transpiration (wall suction/injection) Prandtl number, Brownian motion parameter, thermophoresis parameter and Lewis number on velocity, temperature and concentration functions is illustrated graphically. Transpiration is shown to exert a substantial influence on flow characteristics. Applications of the study include industrial nanotechnological fabrication processes.

Numerical simulation of peristaltic flow of a Carreau nanofluid in an asymmetric channel

Abstract: In this article, we studied MHD peristaltic flow of a Carreau nanofluid in an asymmetric channel. The flow development is carried out in a wave frame of reference moving with velocity of the wave c 1 . The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and then tackled numerically using the fourth and fifth order Runge–Kutta–Fehlberg. Numerical results are obtained for dimensionless velocity, stream function, pressure rise, temperature and nanoparticle volume fraction. It is found that the pressure rise increases with increase in Hartmann Number and thermophoresis parameter.

Blood flow of nanofluid through an artery with composite stenosis and permeable walls

Abstract: This problem deals with the theoretical study of blood flow of nanofluid through composite stenosed arteries with permeable walls. The highly nonlinear momentum equations of nanofluid model are simplified by considering the mild stenosis case. Temperature and nanoparticle equations are coupled; so, we use homotopy perturbation method to calculate the solution of temperature and nanoparticle equations, while the exact solution has been calculated for velocity profile. Also, the expressions for flow impedance, pressure gradient and stream function are computed. These solutions depend on Brownian motion number Nb, thermophoresis number Nt, local temperature Grashof number Gr and local nanoparticle Grashof number Br. The effects of various emerging parameters are discussed through graphs for different values of interest.

Numerical modeling of MHD stability in a cylindrical configuration

Abstract: A numerical modeling of natural convection under the influence of either axial ( B z ) or radial ( B r ) magnetic field in a cylindrical configuration filled with a low-Prandtl number electrically conducting fluid, is studied. The finite volume method is used to discretize the equations of continuity, Navier Stokes and energy. A computer program based on the SIMPLER algorithm is developed. The flow and temperature fields are presented by stream function and isotherms, respectively. Stability diagrams are established according to the numerical results of this investigation. These diagrams put in evidence the dependence of the critical Grashof number, Gr cr with the increase of the Hartmann number, Ha . The strongest stabilization of the convective flows occurs when the magnetic field is applied in the radial direction. This study confirms the possibility of stabilization of a liquid metal flow in natural convection by application of a radial magnetic field.

Peristaltic flow in an asymmetric channel with convective boundary conditions and Joule heating

Abstract: The peristaltic transport of viscous fluid in an asymmetric channel is concentrated. The channel walls exhibit convective boundary conditions. Both cases of hydrodynamic and magnetohydrodynamic (MHD) fluids are considered. Mathematical analysis has been presented in a wave frame of reference. The resulting problems are non-dimensionalized. Long wavelength and low Reynolds number approximations are employed. Joule heating effect on the thermal equation is retained. Analytic solutions for stream function and temperature are constructed. Numerical integration is carried out for pressure rise per wavelength. Effects of influential flow parameters have been pointed out through graphs.

Peristaltic Flow of a Nanofluid under the Effect of Hall Current and Porous Medium

Abstract: The problem of peristaltic flow of an incompressible viscous electrically conducting nanofluid in a vertical asymmetric channel through a porous medium is investigated by taking the Hall effects into account. The governing equations are formulated and simplified under the assumptions of long wavelength and low Reynolds number. The solutions for temperature and nanoparticle profiles are obtained by using the homotopy perturbation method (HPM) and closed form solutions for stream function and pressure gradient are developed. Finally, the effects of various emerging parameters on the physical quantities of interest are plotted and discussed.

Peristaltic flow of couple stress fluid through uniform porous medium

Abstract: Investigation concerning peristaltic motion of couple stress fluid is made. An incompressible couple stress fluid occupies the porous medium. Mathematical analysis is presented through large wavelength and low Reynolds number. Exact analytical expressions of axial velocity, volume flow rate, pressure gradient, and stream function are calculated as a function of couple stress parameter. The essential feature of the analysis is a full description of influence of couple stress parameter and permeability parameter on the pressure, frictional force, mechanical efficiency, and trapping.

Unsteady Conjugate Natural Convection in a Vertical Cylinder Containing a Horizontal Porous Layer: Darcy Model and Brinkman-Extended Darcy Model

Abstract: Transient natural convection in a vertical cylinder partially filled with a porous media with heat-conducting solid walls of finite thickness in conditions of convective heat exchange with an environment has been studied numerically. The Darcy and Brinkman-extended Darcy models with Boussinesq approximation have been used to solve the flow and heat transfer in the porous region. The Oberbeck–Boussinesq equations have been used to describe the flow and heat transfer in the pure fluid region. The Beavers–Joseph empirical boundary condition is considered at the fluid–porous layer interface with the Darcy model. In the case of the Brinkman-extended Darcy model, the two regions are coupled by equating the velocity and stress components at the interface. The governing equations formulated in terms of the dimensionless stream function, vorticity, and temperature have been solved using the finite difference method. The main objective was to investigate the influence of the Darcy number $$10^{-5}\le \hbox {Da}\le 10^{-3}$$ , porous layer height ratio $$0\le d/L\le 1$$ , thermal conductivity ratio $$1\le k_{1,3}\le 20$$ , and dimensionless time $$0\le \tau \le 1000$$ on the fluid flow and heat transfer on the basis of the Darcy and non-Darcy models. Comprehensive analysis of an effect of these key parameters on the Nusselt number at the bottom wall, average temperature in the cylindrical cavity, and maximum absolute value of the stream function has been conducted.

MHD mixed convection stagnation-point flow of a nanofluid over a vertical permeable surface: a comprehensive report of dual solutions

Abstract: The steady laminar magnetohydrodynamic mixed convection boundary layer flow of a nanofluid near the stagnation-point on a vertical permeable plate with prescribed external flow and surface temperature is investigated in this study. Here, both assisting and opposing flows are considered and studied. Using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved numerically using the Runge–Kutta scheme coupled with a conventional shooting procedure. Three different types of nanoparticles, namely copper Cu, alumina Al2O3 and titania TiO2 with water as the base fluid are considered. Numerical results are obtained for the skin-friction coefficient and Nusselt number as well as for the velocity and temperature profiles for some values of the governing parameters, namely, the volume fraction of nanoparticles ϕ, permeability parameter fo, magnetic parameter M and mixed convection parameter λ. It is found that dual solutions exist for both assisting and opposing flows, and the range of the mixed convection parameter for which the solution exists, increases with suction, magnetic field and volume fraction of nanoparticles.

Hydromagnetic effect on inclined peristaltic flow of a couple stress fluid

Abstract: In this paper, we have investigated the effect of channel inclination on the peristaltic transport of a couple stress fluid in the presence of externally applied magnetic field. The slip velocity at the channel wall has been taken into account. Under the long wave length and low-Reynolds number assumptions, the analytical solutions for axial velocity, stream function, pressure gradient and pressure rise are obtained. The computed results are presented graphically by taking valid numerical data for non-dimensional physical parameters available in the existing scientific literatures. The results revealed that the trapping fluid can be eliminated and the central line axial velocity can be reduced with a considerable extent by the application of magnetic field. The flow phenomena for the pumping characteristics, trapping and reflux are furthermore investigated. The study shows that the slip parameter and Froude number play an important role in controlling axial pressure gradient.

Effects of convective conditions and chemical reaction on peristaltic flow of Eyring-Powell fluid

Abstract: This paper addresses the peristaltic flow of Eyring-Powell fluid in a symmetric channel with convective conditions. The Soret and Dufour effects are considered. Impact of first order chemical reaction is seen. The channel walls are of compliant nature. Long wavelength and low Reynolds number concepts are implemented. Resulting problems are solved for the stream function, temperature and concentration. Graphical results are presented and discussed in detail for various pertinent parameters.

Peristaltic Sisko nano fluid in an asymmetric channel

Abstract: The present article deals with the peristaltic flow of a Sisko nanofluid in an asymmetric channel Here the governing flow equations for nano Sisko fluid are formulated in Cartesian coordinates system The flow analysis is developed in a wave frame of reference moving with velocity of the wave c The fourth- and fifth-order Runge–Kutta–Fehlberg method is used to calculate the numerical solutions of simplified coupled nonlinear equations and find the expressions of velocity, stream function, pressure rise, temperature and nanoparticle phenomena graphically Numerical solutions are also presented in tabulated form

Peristaltic Transport of Eyring-Powell Fluid in a Curved Channel

Abstract: In this article, the peristaltic flow of an Eyring-Powell fluid in a curved channel is modeled. Anapproach utilizing along wavelength and low Reynolds number is employed for the analysis in a wave frame. A series solution is obtained. Results for stream function, longitudinal velocity, pressure gradient, and pressure rise are plotted and analyzed. The pressure rise per wavelength is examined numerically. It is noted that results for aplane channel and viscous fluid can be deduced as the limiting cases of the present work. A comparison of flow between the planarand curved channel is also shown.

Numerical simulation of marangoni magnetohydrodynamic bio-nanofluid convection from a non-isothermal surface with magnetic induction effects: a bio-nanomaterial manufacturing transport model

Abstract: Laminar magnetohydrodynamic Marangoni-forced convection boundary layer flow of a water-based biopolymer nanofluid containing nanoparticles from a non-isothermal plate is studied. Magnetic induction effects are incorporated. A variety of nanoparticles are studied, specifically, silver, copper, aluminium oxide and titanium oxide. The Tiwari–Das model is utilized for simulating nanofluid effects. The normalized ordinary differential boundary layer equations (mass, magnetic field continuity, momentum, induced magnetic field and energy conservation) are solved subject to appropriate boundary conditions using Maple shooting quadrature. The influence of Prandtl number (Pr), magnetohydrodynamic body force parameter (β), reciprocal of magnetic Prandtl number (α) and nanofluid solid volume fraction (φ) on velocity, temperature and magnetic stream function distributions is investigated in the presence of strong Marangoni effects (ξ i.e., Marangoni parameter is set as unity). Magnetic stream function is accentuated with body force parameter. The flow is considerably decelerated as is magnetic stream function gradient, with increasing nanofluid solid volume fraction, whereas temperatures are significantly enhanced. Interesting features in the flow regime are explored. The study finds applications in the fabrication of complex biomedical nanofluids, biopolymers, etc.

The effect of thermal radiation on the natural convection boundary layer flow over a wavy horizontal surface

Abstract: In this article, natural convection boundary layer flow is investigated over a semi-infinite horizontal wavy surface. Such an irregular (wavy) surface is used to exchange heat with an external radiating fluid which obeys Rosseland diffusion approximation. The boundary layer equations are cast into dimensionless form by introducing appropriate scaling. Primitive variable formulations (PVF) and stream function formulations (SFF) are independently used to transform the boundary layer equations into convenient form. The equations obtained from the former formulations are integrated numerically via implicit finite difference iterative scheme whereas equations obtained from lateral formulations are simulated through Keller-box scheme. To validate the results, solutions produced by above two methods are compared graphically. The main parameters: thermal radiation parameter and amplitude of the wavy surface are discussed categorically in terms of shear stress and rate of heat transfer. It is found that wavy surface increases heat transfer rate compared to the smooth wall. Thus optimum heat transfer is accomplished when irregular surface is considered. It is also established that high amplitude of the wavy surface in the boundary layer leads to separation of fluid from the plate.

Peristaltic motion of third grade fluid in curved channel

Abstract: Analysis is performed to study the slip effects on the peristaltic flow of non-Newtonian fluid in a curved channel with wall properties. The resulting nonlinear partial differential equations are transformed to a single ordinary differential equation in a stream function by using the assumptions of long wavelength and low Reynolds number. This differential equation is solved numerically by employing the built-in routine for solving nonlinear boundary value problems (BVPs) through the software Mathematica. In addition, the analytic solutions for small Deborah number are computed with a regular perturbation technique. It is noticed that the symmetry of bolus is destroyed in a curved channel. An intensification in the slip effect results in a larger magnitude of axial velocity. Further, the size and circulation of the trapped boluses increase with an increase in the slip parameter. Different from the case of planar channel, the axial velocity profiles are tilted towards the lower part of the channel. A comparative study between analytic and numerical solutions shows excellent agreement.

Subsonic Solutions for Steady Euler--Poisson System in Two-Dimensional Nozzles

Abstract: In this paper, we prove the existence and stability of subsonic flows for a steady full Euler--Poisson system in a two-dimensional nozzle of finite length when imposing the electric potential difference on a noninsulated boundary from a fixed point at the entrance, and prescribing pressure at the exit of the nozzle. The Euler--Poisson system for subsonic flow is a hyperbolic-elliptic coupled nonlinear system. One of the crucial ingredients of this work is the combination of Helmholtz decomposition for the velocity field and stream function formulation. In terms of the Helmholtz decomposition, the Euler--Poisson system is rewritten as a second order nonlinear elliptic system of three equations and transport equations for entropy and pseudo-Bernoulli's invariant. The associated elliptic system in a Lipschitz domain with nonlinear boundary conditions is solved with the help of the estimates developed in [M. Bae, B. Duan, and C. J. Xie, Existence and Stability of Multidimensional Steady Potential Flows for Eu...

Multiple-relaxation-time lattice Boltzmann method for study of two-lid-driven cavity flow solution multiplicity

Abstract: As a fundamental subject in fluid mechanics, sophisticated cavity flow patterns due to the movement of multi-lids have been routinely analyzed by the computational fluid dynamics community. Unlike those reported computational studies that were conducted using more conventional numerical methods, this paper features employing the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) to numerically investigate the two-dimensional cavity flows generated by the movements of two adjacent lids. The obtained MRT-LBM results reveal a number of important bifurcation flow features, such as the symmetry and steadiness of cavity flows at low Reynolds numbers, the multiplicity of stable cavity flow patterns when the Reynolds number exceeds its first critical value, as well as the periodicity of the cavity flow after the second critical Reynolds number is reached. Detailed flow characteristics are reported that include the critical Reynolds numbers, the locations of the vortex centers, and the values of stream function at the vortex centers. Through systematic comparison against the simulation results obtained elsewhere by using the lattice Bhatnagar–Gross–Krook model and other numerical schemes, not only does the MRT-LBM approach exhibit fairly satisfactory accuracy, but also demonstrates its remarkable flexibility that renders the adjustment of its multiple relaxation factors fully manageable and, thus, particularly accommodates the need of effectively investigating the multiplicity of flow patterns with complex behaviors.

Slip Effects on MHD Peristaltic Motion with Heat and Mass Transfer

Abstract: This investigation looks at the magnetohydrodynamic peristaltic flow of a viscous fluid occupying a porous space. Channel walls are compliant and the velocity, temperature and concentration slip effects are taken into account. Heat and mass transfer effects are present. Long wavelength approach is utilized in the mathematical description of arising problem. Expressions for stream function, temperature, concentration field and heat transfer coefficient are prepared. The role of key parameters is carefully analyzed. The velocity, temperature and absolute concentration distributions are found to decrease upon increasing the strength of magnetic field. This study reduces to the investigation of Kothandapani and Srinivas (Appl Math Comput 213:197–208, 2009) by neglecting the slip effects.

On some new exact solutions of incompressible steady state Navier-Stokes equations

Abstract: In the present work, Lie symmetries are constructed for the steady state incompressible Navier-Stokes equations in two dimensional space. The Navier-Stokes equations are transformed into a fourth order quasilinear partial differential equation through well known approach of stream function. Seven similarity solutions are obtained using one-parameter Lie group of transformations with commuting infinitesimal operators. Among the seven solutions so obtained, three are new and analysed physically. Also, the remaining four solutions are reported in Polyanin and Zaitsev (Handbook of nonlinear partial differential equations, Chapman and Hall/CRC Press, Boca Raton, pp. 607–608, 2004) and interpreted hydrostatically.