We study the linear stability of a family of jeffery-hamel solutions which satisfy a zero flux condition with a suitable regularization of these velocity profiles we show that the linearized perturbation equation is well-posed on a weighted l² space with a certain class of radial weights, in the example of a half plane or in the. Keywords mhd electroosmosis jeffery–hamel flow nano fluid slip conditions friction nonlinear ordinary differential equations analytical solution approximate solutions 1 introduction nano fluid mechanics interactions between various fluids type and different surfaces of various geometries have been investigated. Abstractin this paper, the optimal homotopy perturbation method (ohpm) is employed to determine an analytic approximate solution for the nonlinear mhd jeffery-hamel flow and heat transfer problem the navier-stokes equations, taking into account maxwell's electromagnetism and heat transfer, lead to. The jeffery-hamel solutions for plane, viscous, source or sink flow between straight walls are not unique in this paper these solutions are regarded as providing the leading term of a series solution for a class of channels with walls that are nearly straight in a certain sense, but are such that the fluid is not required to emerge. Jeffery–hamel flow rvim nonlinear ordinary differential equation nanofluid a b s t r a c t many researchers have been interested in application of mathematical methods to find analytical solutions of nonlinear equations and for this purpose, new methods have been developed one of the newest analytical methods. Sketches of the radial flow profile associated with each solution branch the labels refer to the classification of the different flows given by fraenkel (1962) fluid between two semi-infinite diverging planes jeffery–hamel flows were first documented almost a century ago (jeffery 1915 hamel 1916), since which time. 21 (2014), 61–77 jeffery-hamel's flows in the plane by teppei kobayashi abstract we consider a radial steady flow of an incompressible viscous fluid which either converges or diverges in a two dimensional wedge domain we prove the existence of a solution to the stationary navier-stokes equations for the restricted. In fluid dynamics jeffery–hamel flow is a flow created by a converging or diverging channel with a source or sink of fluid volume at the point of intersection of the two plane walls it is named after george barker jeffery(1915) and georg hamel(1917), but it has subsequently been studied by many major scientists such as von.
Layer thickness decreased with increase of reynolds number and nanoparticle volume friction and increased with increasing hartmann number keywords: nanofluid magneto hydro dynamic jeffery–hamel flow nonlinear ordinary differential equation homotopy perturbation method 1 inroduction in fluid mechanics. Abstract: in this study, stochastic numerical treatment is presented for boundary value problems (bvps) arising in nanofluidics for nonlinear jeffery–hamel flow ( nj-hf) equations using feed-forward artificial neural networks (anns) optimized with bio- inspired computing based on genetic algorithms (gas. Limit is first treated in the context of flow in a channel of slowly varying width the jeffery-hamel problem proper is treated in $$3-6, and the effect of varying the viscosity ratio h in a two-fluid situation is studied in $5, results already familiar in the single-fluid context are recapitulated and reformulated in a. Paper the jeffery-hamel flow-a nonlinear equation of 3rd order-is studied by homotopy perturbation method after introducing homo- topy perturbation method and the way of obtaining adomian's poly- nomial, we solved the problem for divergent and convergent channel finally, velocity distribution and shear stress.
The effects of nanoparticles and magnetic field on the nonlinear jeffery-hamel flow using cuwater nanofluid are analysed in the present study the basic dimensionless governing equations are solved using power series, which is then analysed by applying a semi-numerical analytical technique called hermite- padé. This paper presents a new linear theory of small two-dimensional perturbations of a jeffery-hamel flow of a viscous incompressible fluid, in order to understand better the stability of the steady flow driven between inclined plane walls by a line source at the intersection of the walls because the variables of space and time. The extended bernoulli equation is formulated in an exact form for a microscopic and small reynolds number jeffery-hamel flow in a two-dimensional convergent or divergent channel the friction loss and the friction coefficient derived from the extended bernoulli equation are also obtained for the purpose of engineering.
This paper aims to find the exact solution in an implicit form for the well-known nonlinear boundary value problem, namely the mhd jeffery-hamel problem, which can be described as the flow between two planes that meet at an angle also, two accurate approximate analytic solutions (series solution) are obtained by the. The authors give the exact solution for the thermal distribu- tions for the steady laminar flow of a viscous incompressible fluid between nonparallel plane walls held at a constant temperature the velocity profiles are determined with the aid of jacobian elliptic functions by using the jeffery-hamel solution of. In this study of the temporal stability of jeffery–hamel flow, the critical reynolds number based on the volume flux, rc, and that based on the axial velocity, rec, are computed it is found that both critical reynolds numbers decrease very rapidly when the half-angle of the channel, α, increases, such that the. Introduction the flow between two planes that meet at an angle was first analyzed by jeffery (1915) and hamel (1916) under suitable assumptions, the problem can be reduced to the solution of an ordinary differential equation this ode can be readily solved using various numerical techniques.
A jeffery-hamel (j-h) flow model of the non-newtonian fluid type inside a convergent wedge (inclined walls) with a wall friction is derived by a nonlinear ordinary differential equation with.
Three new analytical approximate techniques for addressing nonlinear problems are applied to jeffery–hamel flow homotopy analysis method (ham), homotopy perturbation method (hpm) and differential transformation method (dtm) are proposed and used in this research these methods are very useful and. The present article addresses jeffery-hamel flow: fluid flow between two rigid plane walls, where the angle between them is [email protected] a new analytical method called the optimal homotopy asymptotic method (oham) is briefly introduced, and then employed to solve the governing equation the validity of the. The classical jeffery-hamel flow due to a point source or sink in convergent/ divergent channels is extended in this paper for the first time in the literature to the case where the stationary channel walls are permitted to stretch or shrink such a physical mechanism is characterised by means of a parameter in the wall boundary.