Showing papers on "Stream function published in 2013"

Numerical study of Williamson nano fluid flow in an asymmetric channel

Abstract: This article investigates with the peristaltic flow of a Williamson nano fluid in an asymmetric channel. The related modeling of the problem has been done in Cartesian coordinate system. Problem has been simplified with the reliable assumptions i.e. long wave length and small Reynolds number. Numerical solutions have been evaluated for stream function, velocity profile, temperature profile, nano particle phenomena and pressure rise. Graphical results have been presented and discussed for various involved parameters.

Mhd eyring–prandtl fluid flow with convective boundary conditions in small intestines

Abstract: In this paper, we have discussed the food movement in stomach with thermal boundary conditions. Eyring–Prandtl fluid model is considered. Formulation of the considered phenomena have been developed for both fixed and moving frame of references. Regular perturbation is used to find the solution of stream function, temperature profile and pressure gradient. Analysis has been carried out for velocity, "stream function, temperature, pressure gradient and heat transfer". Appearance of pressure gradient is quite complicated so to get the expression for pressure rise we have used numerical integration. It is perceived that the velocity close to the channel walls is not same in outlook of the Eyring–Prandtl fluid parameter taken as β and Hartman number M. The velocity decreases by increasing β and M.

An analytical solution for Dean flow in curved ducts with rectangular cross section

Abstract: In this paper, a full analytical solution for incompressible flow inside the curved ducts with rectangular cross-section is presented for the first time. The perturbation method is applied to solve the governing equations and curvature ratio is considered as the perturbation parameter. The previous perturbation solutions are usually restricted to the flow in curved circular or annular pipes related to the overly complex form of solutions or singularity situation for flow in curved ducts with non-circular shapes of cross section. This issue specifies the importance of analytical studies in the field of Dean flow inside the non-circular ducts. In this study, the main flow velocity, stream function of lateral velocities (secondary flows), and flow resistance ratio in rectangular curved ducts are obtained analytically. The effect of duct curvature and aspect ratio on flow field is investigated as well. Moreover, it is important to mention that the current analytical solution is able to simulate the Taylor-Gortler and Dean vortices (vortices in stable and unstable situations) in curved channels.

Numerical simulation of turbulent plume spread in ceiling vented enclosure

Abstract: The buoyancy-induced turbulent flow generated by a heat source in a square enclosure with single and multiple ceiling vents has been studied numerically. A two-dimensional, turbulent natural convection flow is investigated in stream function and vorticity formulation approach. A low Reynolds number k – ϵ turbulence model of Lam Bremhorst is used to solve the governing equations using high accuracy compact finite difference schemes. Results are reported for different Grashof numbers varied from 10 8 to 10 10 . The effects of heat source location, vent location and multiple vents on flow characteristics in enclosure are presented. The heat transfer characteristics, ambient entrainment flow rate and the oscillatory nature of the penetrative and recirculating flow inside the vented enclosure are reported. The results indicate significant change in the flow behavior by varying the location of heat source and vent for fixed Grashof number. The effect of entrainment of ambient air is significant with increase in Grashof number. The volume flow rates through the two ceiling vents showed a significant variation depending on the location of vent. Present results are matching very well with the experimental and numerical results available from the literature.

Peristaltic Flow of a Non-Newtonian Fluid in an Asymmetric Channel with Convective Boundary Conditions

Abstract: This article addresses peristaltic flow of third order fluid in an asymmetric channel. Channel walls are subjected to the convective boundary conditions. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. Long wavelength approximation and perturbation method give the series solutions for the stream function, temperature and longitudinal pressure gradient. Analysis has been further carried out for pressure rise per wavelength through numerical integration. Several graphs of physical interest are displayed and discussed.

Peristaltic flow of MHD Eyring-Powell fluid in a channel

Abstract: Peristaltic transport of Eyring-Powell fluid is investigated in the presence of an induced magnetic field. The fluid is considered in a channel with non-conducting walls. Mathematical modelling is given subject to the long wavelength and low Reynolds number assumptions. The resulting non-linear system is solved for the stream function, pressure gradient, magnetic force function, induced magnetic field and current density distributions. The flow quantities have been examined for various parameters. The pressure rise per wavelength is also analyzed.

On Stationary Solutions of Two-Dimensional Euler Equation

Abstract: We study the geometry of streamlines and stability properties for steady state solutions of the Euler equations for an ideal fluid.

A compact streamfunction-velocity scheme on nonuniform grids for the 2D steady incompressible Navier-Stokes equations

Abstract: In this paper, an effective compact finite difference approximation which carries streamfunction and its first derivatives (velocities) as the unknown variables for the streamfunction-velocity formulation of the steady two dimensional incompressible Navier-Stokes equation is developed on non-uniform orthogonal Cartesian grids. To solve the resulting system of equations, a multigrid iterative strategy on nonuniform grids is introduced by using the interpolation techniques. Numerical experiments, involving two test problems with analytical solutions and the lid-driven square cavity flow problem are carried out to display the superiority of the currently developed method on nonuniform grid. Numerical results show that the present method on nonuniform grids gets as similarly efficient convergence rate as on uniform grids, viz., second order accuracy and the resolution of the computed solutions for the problems with the sharp changes can be significantly improved when the nonuniform grid strategy is utilized. The backward-facing step flow is also calculated by the present method to exhibit the capability to simulate the distant field using fewer grid points. The solution for the natural convection problem reveals further the wide applications of the present method not only in the flow problems but also in the heat transfer problems. All of these numerical results demonstrate the accuracy and efficiency of the currently proposed schemes.

A non‐conforming least‐squares finite element method for incompressible fluid flow problems

Abstract: SUMMARY In this paper, we develop least-squares finite element methods (LSFEMs) for incompressible fluid flows with improved mass conservation. Specifically, we formulate a new locally conservative LSFEM for the velocity–vorticity–pressure Stokes system, which uses a piecewise divergence-free basis for the velocity and standard C0 elements for the vorticity and the pressure. The new method, which we term dV-VP improves upon our previous discontinuous stream-function formulation in several ways. The use of a velocity basis, instead of a stream function, simplifies the imposition and implementation of the velocity boundary condition, and eliminates second-order terms from the least-squares functional. Moreover, the size of the resulting discrete problem is reduced because the piecewise solenoidal velocity element is approximately one-half of the dimension of a stream-function element of equal accuracy. In two dimensions, the discontinuous stream-function LSFEM [1] motivates modification of our functional, which further improves the conservation of mass. We briefly discuss the extension of this modification to three dimensions. Computational studies demonstrate that the new formulation achieves optimal convergence rates and yields high conservation of mass. We also propose a simple diagonal preconditioner for the dV-VP formulation, which significantly reduces the condition number of the LSFEM problem. Published 2012. This article is a US Government work and is in the public domain in the USA.

Mixed convection heat and mass transfer in peristaltic flow with chemical reaction and inclined magnetic field

Abstract: A mathematical model is constructed to investigate the mixed convective heat and mass transfer effects on peristaltic flow of magnetohydrodynamic pseudoplastic fluid in a symmetric channel. An analysis has been carried out to examine the impact of an inclined magnetic field and chemical reaction in presence of heat sink/source. Mechanics of flow and heat/mass transfer described in terms of continuity, linear momentum, energy and concentration equations are predicted by using long wavelength and low Reynolds number. Expressions for stream function, temperature, concentration and pressure gradient are derived. Numerical simulation is performed for the rise in pressure per wave length. Effects of several physical parameters on the flow quantities are analyzed.

On the appearance of internal wave attractors due to an initial or parametrically excited disturbance

Abstract: In this paper we solve two initial value problems for two-dimensional internal gravity waves. The waves are contained in a uniformly stratified, square-shaped domain whose sidewalls are tilted with respect to the direction of gravity. We consider several disturbances of the initial stream function field and solve both for its free evolution and for its evolution under parametric excitation. We do this by developing a structure-preserving numerical method for internal gravity waves in a two-dimensional stratified fluid domain. We recall the linearized, inviscid Euler–Boussinesq model, identify its Hamiltonian structure, and derive a staggered finite difference scheme that preserves this structure. For the discretized model, the initial condition can be projected onto normal modes whose dynamics is described by independent harmonic oscillators. This fact is used to explain the persistence of various classes of wave attractors in a freely evolving (i.e. unforced) flow. Under parametric forcing, the discrete dynamics can likewise be decoupled into Mathieu equations. The most unstable resonant modes dominate the solution, forming wave attractors.

The analytic solution of Stokes for time-dependent creeping flow around a sphere: Application to linear viscoelasticity as an ingredient for the generalized Stokes–Einstein relation and microrheology analysis

Abstract: Analytic expressions for the transient stream function, transient flow field, and transient pressure field for creeping flow around a sphere are derived. An analytic expression for the total force on the sphere is also found. The approach is essentially that of Stokes from 1856. Aside from the (essentially trivial) generalization to linear viscoelastic fluids, there is nothing novel in the derivation. Our purpose is to (1) point out that Stokes, not Basset or Boussinesq derived it first, (2) show how simple the derivation is, which may be compared to the more famous solution of Landau and Lifshitz, (3) show an application of the correspondence between creeping flow and linear viscoelastic flow solutions, and (4) provide sufficiently detailed notes so that the derivation might be given in a graduate fluid dynamics or transport phenomena lecture.

Slow Motion of a Porous Cylindrical Shell in a concentric cylindrical cavity

Abstract: This paper concerns the Slow Motion of a Porous Cylindrical Shell in a concentric cylindrical cavity using particle-in-cell method. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid in their stream function formulations are used. The hydrodynamic drag force acting on each porous cylindrical particle in a cell and permeability of membrane built up by cylindrical particles with a porous shell are evaluated. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta-Morse’s condition). Some previous results for hydrodynamic drag force and dimensionless hydrodynamic permeability have been verified. Variation of the drag coefficient and dimensionless hydrodynamic permeability with permeability parameter σ, particle volume fraction γ has been studied and some new results are reported. The flow patterns through the regions have been analyzed by stream lines. Effect of particle volume fraction γ and permeability parameter σ on flow pattern is also discussed. In our opinion, these results will have significant contributions in studying, Stokes flow through cylindrical swarms.

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 steady full Euler-Poisson system in a two dimensional nozzle of finite length when imposing the electric potential difference on non-insulated boundary from a fixed point at the entrance, and prescribing the 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 ingredient of this work is the combination of Helmholtz decomposition for the velocity field and stream function formulation together. 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 [2] based on its nice structure. The transport equations are resolved via the flow map induced by the stream function formulation. Furthermore, the delicate estimates for the flow map give the uniqueness of the solutions.

A framework for estimating potential fluid flow from digital imagery.

Abstract: Given image data of a fluid flow, the flow field, ⟨u,v⟩, governing the evolution of the system can be estimated using a variational approach to optical flow. Assuming that the flow field governing the advection is the symplectic gradient of a stream function or the gradient of a potential function—both falling under the category of a potential flow—it is natural to re-frame the optical flow problem to reconstruct the stream or potential function directly rather than the components of the flow individually. There are several advantages to this framework. Minimizing a functional based on the stream or potential function rather than based on the components of the flow will ensure that the computed flow is a potential flow. Next, this approach allows a more natural method for imposing scientific priors on the computed flow, via regularization of the optical flow functional. Also, this paradigm shift gives a framework—rather than an algorithm—and can be applied to nearly any existing variational optical flow t...

On hydrodynamic permeability of a membrane built up by porous deformed spheroidal particles

Abstract: This paper concerns the slow viscous flow of an incompressible fluid past a swarm of identically oriented porous deformed spheroidal particles, using particle-in-cell method. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid region in their stream function formulations are used. Explicit expressions are investigated for both the inside and outside flow fields to the first order in a small parameter characterizing the deformation. The flow through the porous oblate spheroid is considered as the particular case of the porous deformed spheroid. The hydrodynamic drag force experienced by a porous oblate spheroid and permeability of a membrane built up by porous oblate spheroids having parallel axis are evaluated. The dependence of the hydrodynamic drag force and the hydrodynamic permeability on particle volume fraction, deformation parameter and viscosity of porous fluid are also discussed. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta-Morse’s condition). Some previous results for hydrodynamic drag force and hydrodynamic permeability have been verified. The model suggested can be used for evaluation of changing hydrodynamic permeability of a membrane under applying unidirectional loading in pressure-driven processes (reverse osmosis, nano-, ultra- and microfiltration).

Regularity of traveling periodic stratified water waves with vorticity

Abstract: We prove real analyticity of all the streamlines, including the free surface, of a steady stratified flow of water over a flat bed in the absence of stagnation points, with a Holder continuous Bernoulli function and a Holder continuously differentiable density function. Furthermore, we show that if the Bernoulli function and the density function possess some Gevrey regularity of index s , then the stream function admits the same Gevrey regularity throughout the fluid domain; in particular if the Gevrey index s equals to 1, then we obtain analyticity of the stream function. The regularity results hold for three distinct physical regimes: capillary, capillary-gravity, and gravity water waves.

Convective heat transfer analysis on Prandtl fluid model with peristalsis

Abstract: The effects of magnetohydrodynamic MHD on peristaltic transport of Prandtl fluid in a symmetric channel have been studied under the assumptions of long wave length and low-Reynolds number. Channel walls are considered compliant in nature. Series solutions of axial velocity, stream function and temperature are given by using regular perturbation technique for small values of Prandtl fluid parameter. The effects of physical parameters on the velocity, streamlines and temperature are examined by plotting graphs.

Regularity of Traveling Free Surface Water Waves with Vorticity

Abstract: We prove real analyticity of all the streamlines, including the free surface, of a gravity- or capillary-gravity-driven steady flow of water over a flat bed, with a Holder continuous vorticity function, provided that the propagating speed of the wave on the free surface exceeds the horizontal fluid velocity throughout the flow. Furthermore, if the vorticity possesses some Gevrey regularity of index s, then the stream function of class C 2,μ admits the same Gevrey regularity throughout the fluid domain; in particular if the Gevrey index s equals 1, then we obtain analyticity of the stream function. The regularity results hold not only for periodic or solitary-water waves, but also for any solution to the hydrodynamic equations of class C 2,μ .

Effects of rotation and magnetic field on the nonlinear peristaltic flow of a second-order fluid in an asymmetric channel through a porous medium

Abstract: In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically The material is represented by the constitutive equations for a second-order fluid Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically Numerical results are given and illustrated graphically in each case considered Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena

Flow of MHD Carreau fluid in a curved channel

Abstract: Analysis has been made for the curvature effects on the MHD peristaltic flow of an incompressible Carreau fluid in a channel. The flow problem is first reduced in the wave frame of reference and then solved after employing the long wavelength and low Reynolds number approximations. Expressions of stream function, pressure gradient, magnetic force function, induced magnetic field and current density are derived and then examined for various parameters of interest.