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The purpose of this paper is to demonstrate the eligibility of the weighted residual methods (WRMs) applied to Jeffery-Hamel Flow. Selecting the most appropriate method among the WRMs and discussing about Jeffery-Hamel flow's treatment in divergent and convergent channels are the other important purposes of the present research.

Three analytical methods (collocation, Galerkin and least square method) have been applied to solve the governing equations. The reliability of the methods is also approved by a comparison made between the forth order Runge-Kutta numerical method.

The obtained solutions revealed that WRMs can be simple, powerful and efficient techniques for finding analytical solutions in science and engineering non-linear differential equations.

It could be considered as a first endeavor to use the solution of the Jeffery-Hamel flow using these kind of analytical methods along with the numerical approach.

The main purpose of the work is to demonstrate the eligibility of the methods applied and to have the more reliable and user friendly approaches to find the solution of the applicable governing equations such as of the MHD flow.

The numerical and semi analytical methods have been applied to solve the governing equations. The reliability of the methods is also approved by a comparison made between the results obtained and the results of the former studies performed using the other numerical approach.

The reliability of the methods are approved, so that the method could be used to discuss more in depth arguments on the different profiles of the solution.

It could be considered as a first endeavor to use the solution of the MHD Jeffery Hamel flow using this kind of numerical method along with the semi analytical approach.

The purpose of this paper is to find a solution of laminar liquid flow in asymmetric narrow channels. In many cases, an intuitive solution is much more useful and necessary for engineering applications, although numerical solutions can be obtained.

The Navier‐Stokes equations of laminar liquid flow in asymmetric narrow channels are simplified based on geometric characteristics of narrow channels, physical characteristics of liquid and boundary conditions. The simplified Navier‐Stokes equations are solved theoretically. Verification of the obtained results is carried out based on comparing with the Jeffery‐Hamel flow, which is an exact solution of liquid flow in convergent or divergent channels proposed by Jeffery.

This paper proposed an intuitive solution of laminar liquid flow in asymmetric narrow channels. Obtained results show that the solution can provide a fairly precise flowrate, when a ratio between the width of the channel and the curvature of the boundary of the asymmetry channel is smaller than 0.2936/Re. Furthermore, the obtained solution of pressure distribution along the channel shows high enough accuracy, even though the Reynolds number reaches to higher than 105.

Because the authors assumed the width of the channel is far smaller than the curvature of the boundary of the asymmetric channel, the obtained results could only fit finite cases. Because the Navier‐Stocks equations were finally simplified into one‐dimensional, it is impossible to forecast separation flows; so the obtained results will fail when the Re number is too big. However, experiments should be carried out further to verify these problems.

This paper proposes an intuitive solution of laminar liquid flow in asymmetric narrow channels, including the pressure distribution along the channel.

The purpose of this paper is to study and analyze the converging/diverging channel flow and heat transfer with the multiple slips effect, which is a development of the Jeffery–Hamel problem using the mass-based hybrid nanofluid algorithm. Whereas transferring biological liquid by arteries is a vital issue, mathematical modeling of hybrid nanofluid flow containing titanium dioxide and silver as nanoparticles and blood as base liquid through a converging/diverging duct, which can be a useful analysis for the fields of drug delivery, has been investigated.

The present approach is based on the Tiwari–Das nanofluid method. In this modeling, the volume fraction of nanoparticles is replaced with nanoparticles masses. The partial differential equations of the mass, momentum and energy conservations are changed to the system of ordinary differential equations through the similarity solution method. The final governing equations are solved by Runge–Kutta–Fehlberg procedure and shooting method.

The effect of emerging parameters on the temperature, the velocity, the Nusselt number and the skin friction have been analyzed by graphical and tabular reports. It is observed that the opposition to hybrid nanofluid flow in the attendance of particles of nonspherical shapes is more enhanced than those in the attendance of particles of spherical shapes. This issue demonstrates that the rheology of a hybrid nanofluid is dependent on the shape of particles. Besides, backflow regimes form in the divergent channel for high values of Reynolds number, m₂ and a. Indeed, this modeling for the hybrid nanofluid can be useful in different technologies and industries such as biological ones. It is worth mentioning that the excellent achievement of the mass-based algorithm for heat transfer and hybrid nanofluid flow is the most important success of this study.

The main originality is related to the development of the Jeffery–Hamel problem using the mass-based hybrid nanofluid algorithm. This new mass-based method is a single-phase hybrid nanofluid approach that the inputs are masses of nanoparticles and base liquid. Besides, considering the multiple slips effect and also pure blood as base fluid in this problem are also new.

The purpose of this paper is to demonstrate the eligibility of the Weighted Residual Methods (WRMs) applied to magneto hydro dynamic (MHD) nanofluid flow in divergent and convergent channels. Selecting the most appropriate method among the WRMs and discussing about Jeffery-Hamel flow's treatment in divergent and convergent channels are the other important purposes of the present research.

Three analytical methods (Collocation, Galerkin and Least Square Method) and numerical method have been applied to solve the governing equations. The reliability of the methods is also approved by a comparison made between the fourth-order Runge-Kutta numerical method.

The obtained solutions revealed that WRMs can be simple, powerful and efficient techniques for finding analytical solutions in science and engineering non-linear differential equations.

It could be considered as a first endeavor to use the solution of the MHD nanofluid flow in divergent and convergent channels using these kinds of analytical methods along with the numerical approach.

The objective of the present study is to investigate the effect of arbitrary magnetic Reynolds number on steady flow of an incompressible conducting viscous liquid in convergent‐divergent channels under the influence of an externally applied homogeneous magnetic field.

The solution of the non‐linear 2D Navier‐Stokes equations modeling the flow field is obtained using a perturbation technique coupled with a special type of Hermite‐Padé approximation method implemented numerically on MAPLE and a bifurcation study is performed.

The results show that increasing values of magnetic Reynolds number causes a general decrease in the fluid velocity around the central region of the channel. The flow reversal control is also observed by increasing magnetic field intensity. The bifurcation study reveals the solution branches and turning points.

The reported results are very useful in the field of engineering flow control and industrial metal casting for the control of molten metal flows.

Effect of arbitrary magnetic Reynolds on the overall flow structure in converging‐diverging channels are presented and studied using a newly developed numerical approach.

The 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).

A 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.

To 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.

The 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.

The purpose of this paper is to analyse the force convection laminar boundary layer flow on irregular boundary in diverging channel with the presence of magnetic field effects. Effects of various fluid parameters such as suction/injection, viscous dissipation, magnetic parameter and heat source/sink on velocity and temperature profiles are numerically analyzed. Moreover, numerically investigated on skin-friction and heat transfer coefficients when suction/injection occur.

The governing coupled partial differential equations are transformed to dimensionless form using non-similarity transformations. The non-dimensional partial differential equations are linearized by quasi-linearization technique and solved by varga's algorithm with numerical finite difference scheme on a non-uniform mesh.

The computation results are presented in terms of temperature, heat transfer and skin friction coefficients; these are useful for determining surface heat requirements. It was found that, in finite difference scheme for non-uniform mesh with quasi-linearization technique method gives smoothness of solution compared to finite difference scheme for uniform mesh, and this evidence is graphically represented in Figure 2.

The impacts of viscous dissipation (Ec) and magnetic parameter (Ha) on temperature profiles, skin friction and heat transfer are analyzed, which determine the heat generation/absorption to ensure the MHD flow of the laminar boundary layer on irregular boundary over a diverging channel.

This paper aims to investigate a linear and temporal stability analysis of hybrid nanofluid flow between two parallel plates filled with a porous medium and whose lower plate is fixed and the upper plate animated by a uniform rectilinear motion.

The nanofluid is composed of water as a regular fluid, silver (Ag) and alumina (Al₂O₃) as nanoparticles. The mathematical model takes into account other effects such as the magnetic field and the aspiration (injection/suction). Under the assumption of a low magnetic Reynolds number, a modified Orr–Sommerfeld-type eigenvalue differential equation governing flow stability was derived and solved numerically by Chebyshev’s spectral collocation method. The effects of parameters such as volume fraction, Darcy number, injection/suction Reynolds number, Hartmann number were analyzed.

It was found the following: the Darcy number affects the stability of the flow, the injection/suction Reynolds number has a negligible effect, the volume fraction damped disturbances and the magnetic field plays a very important role in enlarging the area of flow stability.

The originality of this work resides in the linear and temporal stability analysis of hydromagnetic Couette flow for hybrid nanofluid through porous media with small suction and injection effects.