Jeffery-Hamel Flow Research Articles

Homotopy analysis method for predicting multiple solutions in the channel flow with stability analysis

The present theoretical investigation covers a study of finding the multiple solutions of a Jeffery–Hamel flow and heat transfer under the influence of magnetic field. An analytical technique (Homotopy Analysis Method) is applied to solve the cylindrical form of governing equations after getting non-dimensional system using suitable transformation. It is noticed that dual solutions exist only for convergent channel case. Critical values of channel angle (αc) are obtained which reveals the existence domain (αc < α < 0) for multiple solutions in convergent channel flow. Stability analysis is also performed by constructing eigenvalue problem to predict the physically stable solution. The minimum positive eigenvalue justifies the fact that the growth of disturbances given to the solution decays with time. The effect of various pertinent physical parameters is shown graphically on velocity, temperature, skin friction coefficient and Nusselt number.

Numerical simulation for Jeffery-Hamel flow and heat transfer of micropolar fluid based on differential evolution algorithm

This article explores the Jeffery-Hamel flow of an incompressible non-Newtonian fluid inside non-parallel walls and observes the influence of heat transfer in the flow field. The fluid is considered to be micropolar fluid that flows in a convergent/divergent channel. The governing nonlinear partial differential equations (PDEs) are converted to nonlinear coupled ordinary differential equations (ODEs) with the help of a suitable similarity transformation. The resulting nonlinear analysis is determined analytically with the utilization of the Taylor optimization method based on differential evolution (DE) algorithm. In order to understand the flow field, the effects of pertinent parameters such as the coupling parameter, spin gradient viscosity parameter and the Reynolds number have been examined on velocity and temperature profiles. It concedes that the good results can be attained by an implementation of the proposed method. Ultimately, the accuracy of the method is confirmed by comparing the present results with the results obtained by Runge-Kutta method.

Some new remarks on MHD Jeffery-Hamel fluid flow problem

Abstract A Hamilton-Poisson realization of the MHD Jeffery-Hamel fluid flow problem is proposed. Tthe nonlinear stability of the equilibrium states is discussed. A comparison between the analytic solutions obtained using the OHAM method and the exact solutions provided by the Hamilton-Poisson realization are presented.

A hybrid computational approach for Jeffery–Hamel flow in non-parallel walls

The key goal of this article is to present an efficient hybrid computational technique, namely homotopy analysis transform method (HATM), to investigate Jeffery–Hamel flow. The HATM is an innovative and efficient amalgamation of homotopy analysis technique, standard Laplace transform scheme and homotopy polynomials. The effect of Reynolds number on velocity profile is studied graphically. The obtained results are compared with existing results and it is noticed that the outcomes are in an excellent agreement. The outcomes of the suggested method reveal that the technique is easy to handle and computationally very fantastic.

Non-modal stability of Jeffery-Hamel flow

The destabilization of modal perturbations in the classical diverging Jeffery-Hamel (JH) flow has been long-known. The converging JH flow is far less-studied, but it is known that convergence suppresses modal instabilities. We make a parallel-flow approximation following previous studies, to examine its non-modal stability at small convergent and divergent angles and show that non-modal growth is extremely sensitive to the angle of convergence/divergence at high Reynolds numbers. The transient growth of energy is significantly suppressed at high Reynolds numbers as the wall angle is varied from divergence to convergence by just a few hundredths of a degree. This finding is especially relevant for convergent channels, where the flow is stable to linear modal perturbations up to the Reynolds numbers of the order of 105 or larger. In all the cases, streamwise-aligned rolls (which are a characteristic of the lift-up mechanism) are the initial perturbations that display the largest energy growth. The spanwise separation between the rolls decreases significantly with channel convergence. Our findings indicate that extremely small imperfections in the wall alignment in channel flows can drastically affect the experimental measurements of algebraic growth of the disturbance kinetic energy, as minute amounts of wall convergence can strongly reduce the maximum transient growth.

Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction

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 appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical (numerical) solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.

Shooting homotopy analysis method

PurposeThe purpose of this paper is to present a new method based on the homotopy analysis method (HAM) with the aim of fast searching and calculating multiple solutions of nonlinear boundary value problems (NBVPs).Design/methodology/approachA major problem with the previously modified HAM, namely, predictor homotopy analysis method, which is used to predict multiplicity of solutions of NBVPs, is a time-consuming computation of high-order HAM-approximate solutions due to a symbolic variable namely “prescribed parameter”. The proposed new technique which is based on traditional shooting method, and the HAM cuts the dependency on the prescribed parameter.FindingsTo demonstrate the computational efficiency, the mentioned method is implemented on three important nonlinear exactly solvable differential equations, namely, the nonlinear MHD Jeffery–Hamel flow problem, the nonlinear boundary value problem arising in heat transfer and the strongly nonlinear Bratu problem.Originality/valueThe more high-order approximate solutions are computable, multiple solutions are easily searched and discovered and the more accurate solutions can be obtained depending on how nonhomogeneous boundary conditions are transcribed to the homogeneous boundary conditions.

Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem

Abstract In 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 two nonlinear ordinary differential equations. The results obtained by means of OHPM show very good agreement with numerical results and with Homotopy Perturbation Method (HPM) results.

Soret and Dufour effects on Jeffery-Hamel flow of second-grade fluid between convergent/divergent channel with stretchable walls

This article investigates the problem related to Jeffery-Hamel with stretchable walls. The effects of mass and heat transfer are taken into account. Soret, Dufour and viscous dissipation effects are examined to scrutinize the behavior of concentration and temperature profiles between convergent/divergent stretchable channels. By using similarity variables, nonlinear partial differential equations governing the flow are reduced into the nondimensional coupled system of ordinary differential equations. Then, said flow model is tackled analytically and numerically over a prescribed domain. For analytical solution, we employed Homotopy Analysis method while for numerical once, Runge-Kutta scheme is used after reducing the system of ordinary differential equations into system of first order initial value problem. The effects of various dimensionless parameters that ingrained in the velocity, concentration and temperature fields are scrutinized graphically for convergent and divergent stretchable channels. Also, the values of skin friction coefficient, local Nusselt and Sherwood numbers are calculated analytically by using Homotopy Analysis method (HAM) for different physical parameters. Different values of quantities of physical interest (skin friction coefficient, local rate of heat and mass transfer) are tabulated for different ingrained parameters in the flow model. Finally, comparison between present results with already existing results in the literature has been made.

Jeffery–Hamel Flow of Nano Fluid Influenced by Wall Slip Conditions

Jeffery–Hamel Flow of Nano Fluid Influenced by Wall Slip Conditions

Haar wavelet solution of the MHD Jeffery-Hamel flow and heat transfer in Eyring-Powell fluid

This study deals with the numerical investigation of Jeffery-Hamel flow and heat transfer in Eyring-Powell fluid in the presence of an outer magnetic field by using Haar wavelet method. Jeffery-Hamel flows occur in various practical situations involving flow between two non-parallel walls. Applications of such fluids in biological and industrial sciences brought a great concern to the investigation of flow characteristics in converging and diverging channels. A suitable similarity transformation is applied to transform the nonlinear coupled partial differential equations (PDEs) into nonlinear coupled ordinary differential equations (ODEs), which govern the momentum and heat transfer properties of the fluid. Due to the high nonlinearity of resulting coupled ODEs, the exact solution is unlikely. Thus, the solution is approximated using a numerical scheme based on Haar wavelets and the results are verified by comparing with 4th order Runge-Kutta results.

Analytical and numerical investigation of thermal radiation effects on flow of viscous incompressible fluid with stretchable convergent/divergent channels

This article, investigates the flow of a viscous incompressible fluid between two nonparallel plane walls, known as Jeffery-Hamel flow, under the influence of thermal radiation. The walls are capable of stretching and shrinking rectilinearly. With the help of suitable similarity variables, the dimensional partial differential equations, governing the flow, are transformed into a coupled system of ordinary differential equations. The Soret and Dufour effects are also taken into consideration while modeling the flow. The analytical solution of the flow model is then obtained by employing Adomian's decomposition method. The same problem has also been solved numerically with the help of fourth order Runge-Kutta scheme. A comparison between the analytical and numerical solutions has been presented and discussed. The influence of different non-dimensional parameters appearing in the flow model on the velocity, temperature and concentration profiles is discussed with the help of graphs. The rates of heat and mass transfer at the walls are also investigated.

Series Solution of Nanofluid Flow and Heat Transfer Between Stretchable/Shrinkable Inclined Walls

In this research, the steady nanofluid flow and heat transfer characteristics in Jeffery–Hamel flow when the stationary rigid nonparallel plates are permitted to stretch or shrink are investigated. Using appropriate transformations, the momentum and energy equations that govern velocity and temperature fields are converted into nonlinear ordinary differential equations. These resulting equations are solved analytically by applying Adomian decomposition method (ADM) and numerically using a fourth order Runge Kutta method featuring shooting technique. In addition, the skin friction coefficient and the Nusselt number as well as the velocity and temperature profiles are investigated subject to various parameters of interest, namely Reynolds number, Prandtl number, Eckert number, nanoparticle volume fraction and stretching/shrinking parameter. The results indicate that the stretchable or shrinkable walls with the presence of alumina nanoparticles in a water base fluid produces more heat and enhances significantly the heat transfer between nonparallel plane walls. It is also demonstrated that the analytical results match perfectly with those of numerical Runge Kutta method, thus justifying the higher accuracy of the ADM. Finally, a discussion whether the nanofluid problem can be interpreted in terms of regular fluid is given.

Critical Analysis of Magnetohydrodynamic Jeffery-Hamel Flow Using Cu-Water Nanofluid

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 approximation. The velocity profiles are presented in convergentdivergent channels for various values of nanoparticles solid volume fraction, Hartmann number, Reynolds number and channel angle. The dominating singularity behavior of the problem is analysed numerically and graphically for nanofluid. The critical relationships among the parameters are also performed qualitatively with the effect of Cu-nanoparticles.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 111-126

Analytical Investigation of Jeffery–Hamel Flow by Modified Adomian Decomposition Method

Abstract The objective of this paper is to present a reliable approach to compute an approximate analytical solution of magneto-hydrodynamic (MHD) Jeffery–Hamel flow by using a new modification of Adomian decomposition method. The approximate solution of this problem is calculated here in the form of a rapidly convergent series at one and both grid points. Results for velocity profiles in divergent and convergent channels are presented for different values of Hartmann and Reynolds numbers. The validity and applicability of this new technique are illustrated through a comparison between reproducing Kernel Hilbert Space Method (RKHSM) (Inc et al., 2013), Modified Homotopy Perturbation Method (MHPM) (Singh, 2014) and numerical solutions.

Design of bio-inspired computing technique for nanofluidics based on nonlinear Jeffery–Hamel flow equations

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) integrated with the active-set method (ASM). NJ-HF equations associated with both convergent and divergent channels, involving nanoparticles, are derived from the transformation of Navier–Stokes partial differential equations to nonlinear BVPs of third-order ordinary differential equations. The mathematical model of the transformed BVPs is developed with the help of ANNs in an unsupervised manner and the design parameters of these networks are trained with GAs, ASM, and GA–ASM. The design scheme is evaluated for NJ-HF by taking water as a base fluid containing three different types of nanomaterials: copper (Cu), alumina (Al2O3), and titania (TiO2) under various scenarios based on the angle of the channels and Reynolds numbers. Accuracy and convergence of the designed scheme are validated through comparison with standard numerical results using the Adams method.

Magnetohydrodynamic Stability of Jeffery-Hamel Flow using Different Nanoparticles

The effects of nanoparticles and magnetic field on the nonlinear Jeffery-Hamel flow of Cu-water nanofluid are analyzed in the present study. The aThe effects of three different nanoparticles and magnetic field on the nonlinear Jeffery-Hamel flow of water based nanofluid are analyzed in the present study. The basic dimensionless governing equations are solved using series solution which are then analysed to inspect the instability of the problem by a semi-numerical analytical technique called Hermite- Padé approximation. The velocity profiles are presented in convergentdivergent channels for various values of nanoparticles solid volume fraction, Hartmann number, Reynolds number and channel angle. The dominating singularity behavior of the problem is analysed numerically and graphically. The critical relationships among the parameters are also performed qualitatively to observe the behavior of the various nanoparticles.basic dimensionless governing equations are solved using series solution which are then analysed to inspect the instability of the problem by a semi-numerical analytical technique called Hermite- Padé approximation. The velocity profiles are presented in convergent-divergent channels for various values of nanoparticles solid volume fraction, Hartmann number, Reynolds number and channel angle. The dominating singularity behavior of the problem is analysed numerically and graphically. The critical relationships among the parameters are also performed qualitatively to observe the behavior of the nanoparticles.

Heat Transfer in Hydro-Magnetic Jeffery-Hamel Flow

In this research, heat transfer problem in the hydromagnetic Jeffery-Hamel flow is investigated. The mathematical formulation of the studied problem allowed us to obtain a mathematical model for thermal distributions under the effect of an external magnetic field through convergent-divergent channels. Thereafter, the resulting nonlinear differential equations governing velocity and heat transfer have been treated analytically by an efficient mathematical technique, called Adomian decomposition method, and the results show an excellent agreement in comparison with the numerical solution obtained via Runge-Kutta method. On the other hand, it is found that a high magnetic field has a stabilizing effect on thermal distributions for both converging and diverging channels.

Extended Bernoulli equation, friction loss, and friction coefficient for microscopic Jeffery-Hamel flow with small Reynolds number up to O(1)

Extended Bernoulli equation, friction loss, and friction coefficient for microscopic Jeffery-Hamel flow with small Reynolds number up to O(1)

二次元ミクロチャンネルでの定常な極低Re数ながれの抵抗係数

The friction loss and the friction or resistance coefficient derived from the extended Bernoulli equation are obtained for a microscopic and small Reynolds number Jeffery-Hamel flow in a two-dimensional convergent or divergent channel. The assumption of microscopic and low Reynolds number flow enables us to make the analysis simple. The cross-sectional average formulae of the friction loss and the friction coefficient are expressed by the geometry of the channel, i.e., the convergent or divergent angle, the channel length, channel widths at the inlet and the exit of the channel. These formulae include the corresponding well-known ones for the two-dimensional parallel flow, i.e., the two-dimensional Poiseuille flow as a special case where the angle is zero. The friction coefficient drastically increases according to the increase in the angle, especially in a narrow channel region, and attains more than ten times of the friction coefficient for the parallel flow.