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1 – 10 of 96Buhe Eerdun, Qiqige Eerdun, Bala Huhe, Chaolu Temuer and Jing-Yu Wang
The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over…
Abstract
Purpose
The purpose of this paper is to consider a steady two-dimensional magneto-hydrodynamic (MHD) Falkner-Skan boundary layer flow of an incompressible viscous electrically fluid over a permeable wall in the presence of a magnetic field.
Design/methodology/approach
The governing equations of MHD Falkner-Skan flow are transformed into an initial values problem of an ordinary differential equation using the Lie symmetry method which are then solved by He's variational iteration method with He's polynomials.
Findings
The approximate solution is compared with the known solution using the diagonal Pad’e approximants and the geometrical behavior for the values of various parameters. The results reveal the reliability and validity of the present work, and this combinational method can be applied to other nonlinear boundary layer flow problems.
Originality/value
In this paper, an approximate analytical solution of the MHD Falkner-Skan flow problem is obtained by combining the Lie symmetry method with the variational iteration method and He's polynomials.
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Ram Jiwari, Vikas Kumar, Ram Karan and Ali Saleh Alshomrani
This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a…
Abstract
Purpose
This paper aims to deal with two-dimensional magneto-hydrodynamic (MHD) Falkner–Skan boundary layer flow of an incompressible viscous electrically conducting fluid over a permeable wall in the presence of a magnetic field.
Design/methodology/approach
Using the Lie group approach, the Lie algebra of infinitesimal generators of equivalence transformations is constructed for the equation under consideration. Using these suitable similarity transformations, the governing partial differential equations are reduced to linear and nonlinear ordinary differential equations (ODEs). Further, Haar wavelet approach is applied to the reduced ODE under the subalgebra 4.1 for constructing numerical solutions of the flow problem.
Findings
A new type of solutions was obtained of the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis.
Originality/value
To find a solution for the MHD Falkner–Skan boundary layer flow problem using the Haar wavelet quasilinearization approach via Lie symmetric analysis is a new approach for fluid problems.
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Behrouz Raftari, Hojatollah Adibi and Ahmet Yildirim
The purpose of this work is to analytically examine the magnetohydrodynamic (MHD) Falkner‐Skan flow.
Abstract
Purpose
The purpose of this work is to analytically examine the magnetohydrodynamic (MHD) Falkner‐Skan flow.
Design/methodology/approach
The series solution is obtained using the Adomian decomposition method (ADM) coupled with Padé approximants.
Findings
Comparison of the present solutions is made with the results obtained by other applied methods and excellent agreement is noted.
Originality/value
In this work, the MHD Falkner‐Skan flow is examined analytically. The series solution is obtained using the ADM coupled with Padé approximants. Comparison of the present solutions is made with the results obtained by other applied methods and excellent agreement is noted.
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Velinda Calvert and Mohsen Razzaghi
This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD Falkner…
Abstract
Purpose
This paper aims to propose a new numerical method for the solution of the Blasius and magnetohydrodynamic (MHD) Falkner-Skan boundary-layer equations. The Blasius and MHD Falkner-Skan equations are third-order nonlinear boundary value problems on the semi-infinite domain.
Design/methodology/approach
The approach is based upon modified rational Bernoulli functions. The operational matrices of derivative and product of modified rational Bernoulli functions are presented. These matrices together with the collocation method are then utilized to reduce the solution of the Blasius and MHD Falkner-Skan boundary-layer equations to the solution of a system of algebraic equations.
Findings
The method is computationally very attractive and gives very accurate results.
Originality/value
Many problems in science and engineering are set in unbounded domains. One approach to solve these problems is based on rational functions. In this work, a new rational function is used to find solutions of the Blasius and MHD Falkner-Skan boundary-layer equations.
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S. Abbasbandy, T. Hayat, A. Alsaedi and M.M. Rashidi
– In this paper, analysis is presented to investigate the Falkner-Skan flow of magnetohydrodynamic (MHD) Oldroyd-B fluid. The paper aims to discuss these issues.
Abstract
Purpose
In this paper, analysis is presented to investigate the Falkner-Skan flow of magnetohydrodynamic (MHD) Oldroyd-B fluid. The paper aims to discuss these issues.
Design/methodology/approach
In this paper, the authors used two methods: homotopy analysis method and numerical Keller-box method.
Findings
It is observed that skin friction coefficient in Oldroyd-B fluid is larger when compared with viscous fluid. Further, the relaxation and retardation times have opposite effects on the velocity components.
Practical implications
A comparative study between the series and numerical solutions for the skin friction is shown in the paper. The results indicated that both solutions are in well agreement.
Originality/value
This model is investigated for the first time, as the authors know.
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Sihem Gherieb, Mohamed Kezzar, Abdelaziz Nehal and Mohamed Rafik Sari
The purpose of this study is to investigate the magneto-hydrodynamics boundary layer Falkner–Skan flow over a flat plate numerically by using the Runge–Kutta method featuring…
Abstract
Purpose
The purpose of this study is to investigate the magneto-hydrodynamics boundary layer Falkner–Skan flow over a flat plate numerically by using the Runge–Kutta method featuring shooting technique and analytically via a new modified analytical technique called improved generalized Adomian decomposition method (improved-GDM).
Design/methodology/approach
It is well established that the generalized decomposition method (GDM) (Yong-Chang et al., 2008), which uses a new kind of decomposition strategy for the nonlinear function, has proved its efficiency and superiority when compared to the standard ADM method. In this investigation, based on the idea of improved-ADM method developed by Lina and Song (Song and Wang, 2013), the authors proposed a new analytical algorithm of computation named improved-GDM. Thereafter, the proposed algorithm is tested by solving the nonlinear problem of the hydro-magnetic boundary layer flow over a flat plate.
Findings
The proposed improved generalized decomposition method (I-GDM) introduces a convergence-control parameter “ω’’ into the GDM, which accelerates the convergence of solution and reduces considerably the computation time. In fact, the key of this method is mainly based on the best selection of the convergence-control parameter ω.
Originality/value
The paper presents a new efficient algorithm of computation that can be considered as an alternative for solving the nonlinear initial boundary layer value problems. Obtained results show clearly the accuracy of the proposed method.
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Mohamed Kezzar, Nawel Boumaiza, Ismail Tabet and Nourreddine Nafir
This paper aims to traitted the combined effects of ferromagnetic particles and magnetic field on mixed convection in the Falkner Skan equation using analytical solution by the…
Abstract
Purpose
This paper aims to traitted the combined effects of ferromagnetic particles and magnetic field on mixed convection in the Falkner Skan equation using analytical solution by the Duan–Rach method.
Design/methodology/approach
Visualization and grouping of effects of various physical parameters such as electrical conductivity of ferro-particles (electrical conductivity calculated using Maxwell model), ferro fluid volume fraction for Magnetite-Fe3O4-water and magnetic field represented by the Hartmann number in a set of third- and second-order nonlinear coupled ordinary differential equations. This set of equations is analytically processed using the Duan–Rach Approach (DRA).
Findings
Obtained DRA results are validated using a numerical solution (Runge–Kutta–Fehlberg-based shooting method). The main objective of this research is to analyze the influence of physical parameters, in particular electrical conductivity, Ferrofluid volume fraction in the case of Magnetite-Fe3O4-water, in addition to the types of solid nanoparticles and Hartmann number on dynamic and thermal distributions (velocity/temperature). Results of the comparison between the numerical solution (Runge–Kutta–Fehlberg-based shooting method) and the analytical solution (DRA) show that the DRA data are in good agreement with numerical data and available literature.
Originality/value
The study uses Runge–Kutta–Fehlberg-based shooting method) and the analytical solution (DRA) to investigate the effect of mixed convection, in the presence of Ferro particles (Magnetite-Fe3O4) in a basic fluid (water for example) and subjected to an external magnetic field on the Falkner–Skan system.
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This paper aims to describe the laminar flow of Maxwell fluid past a non-isothermal rigid plate with a stream wise pressure gradient. Heat transfer mechanism is analyzed in the…
Abstract
Purpose
This paper aims to describe the laminar flow of Maxwell fluid past a non-isothermal rigid plate with a stream wise pressure gradient. Heat transfer mechanism is analyzed in the context of non-Fourier heat conduction featuring thermal relaxation effects.
Design/methodology/approach
Flow field is permeated to uniform transverse magnetic field. The governing transport equations are changed to globally similar ordinary differential equations, which are tackled analytically by homotopy analysis technique. Homotopy analysis method-Padè approach is used to accelerate the convergence of homotopy solutions. Also, numerical approximations are made by means of shooting method coupled with fifth-order Runge-Kutta method.
Findings
The solutions predict that fluid relaxation time has a tendency to suppress the hydrodynamic boundary layer. Also, heat penetration depth reduces for increasing values of thermal relaxation time. The general trend of wall temperature gradient appears to be similar in Fourier and Cattaneo–Christov models.
Research limitations/implications
An important implication of current research is that the thermal relaxation time considerably alters the temperature and surface heat flux.
Originality/value
Current problem even in case of Newtonian fluid has not been attempted previously.
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A. Zeeshan, Muhammad Imran Khan, R. Ellahi and Zaheer Asghar
This study aims to model the important flow response quantities over a shrinking wedge with the help of response surface methodology (RSM) and an artificial neural network (ANN)…
Abstract
Purpose
This study aims to model the important flow response quantities over a shrinking wedge with the help of response surface methodology (RSM) and an artificial neural network (ANN). An ANN simulation for optimal thermal transport of incompressible viscous fluid under the impact of the magnetic effect (MHD) over a shrinking wedge with sensitivity analysis and optimization with RSM has yet not been investigated. This effort is devoted to filling the gap in existing literature.
Design/methodology/approach
A statistical experimental design is a setup with RSM using a central composite design (CCD). This setup involves the combination of values of input parameters such as porosity, shrinking and magnetic effect. The responses of skin friction coefficient and Nusselt number are required against each parameter combination of the experimental design, which is computed by solving the simplified form of the governing equations using bvp4c (a built-in technique in MATLAB). An empirical model for Cfx and Nux using RSM and ANN adopting the Levenberg–Marquardt algorithm based on trained neural networks (LMA-TNN) is attained. The empirical model for skin friction coefficient and Nusselt number using RSM has 99.96% and 99.99% coefficients of determination, respectively.
Findings
The values of these matrices show the goodness of fit for these quantities. The authors compared the results obtained from bvp4c, RSM and ANN and found them all to be in good agreement. A sensitivity analysis is performed, which shows that Cfx as well as Nux are most affected by porosity. However, they are least affected by magnetic parameters.
Originality/value
This study aims to simulate ANN and sensitivity analysis for optimal thermal transport of magnetic viscous fluid over shrinking wedge.
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S. Abbasbandy, Elyas Shivanian, K. Vajravelu and Sunil Kumar
The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a…
Abstract
Purpose
The purpose of this paper is to present a new approximate analytical procedure to obtain dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain. This method, which is based on Padé-approximation and homotopy–Padé technique, is applied to a model of magnetohydrodynamic Falkner–Skan flow as well. These examples indicate that the method can be successfully applied to solve nonlinear differential equations arising in science and engineering.
Design/methodology/approach
Homotopy–Padé method.
Findings
The main focus of the paper is on the prediction of the multiplicity of the solutions, however we have calculated multiple (dual) solutions of the model problem namely, mixed convection heat transfer in a porous medium.
Research limitations/implications
The authors conjecture here that the combination of traditional–Pade and Hankel–Pade generates a useful procedure to predict multiple solutions and to calculate prescribed parameter with acceptable accuracy as well. Validation of this conjecture for other further examples is a challenging research opportunity.
Social implications
Dual solutions of nonlinear differential equations arising in mixed convection flow in a semi-infinite domain.
Originality/value
In this study, the authors are using two modified methods.
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