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1 – 10 of 295
Article
Publication date: 29 July 2014

Buhe 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…

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 5 June 2017

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 29 March 2011

Mehdi Dehghan, Mehdi Tatari and Asma Azizi

The purpose of this paper is to consider the well‐known Falkner‐Skan equation. This equation appears in the modelling of various phenomena in physics and engineering.

Abstract

Purpose

The purpose of this paper is to consider the well‐known Falkner‐Skan equation. This equation appears in the modelling of various phenomena in physics and engineering.

Design/methodology/approach

The He's variational iteration method which is a very efficient tool for solving different kinds of problems, is employed for solving this problem.

Findings

Some other approaches are introduced to compare the efficiency of the new procedure. Several test examples are given to show the advantages of the present method over other existing techniques.

Originality/value

In this paper, a new and efficient technique is proposed to solve the Falkner‐Skan equation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 19 September 2018

Mehdi Delkhosh, Kourosh Parand and D.D. Ganji

This paper aims to solve the Falkner–Skan problem over an isothermal moving wedge using the combination of the quasilinearization method and the fractional order of…

Abstract

Purpose

This paper aims to solve the Falkner–Skan problem over an isothermal moving wedge using the combination of the quasilinearization method and the fractional order of rational Chebyshev function (FRC) collocation method on a semi-infinite domain.

Design/methodology/approach

The quasilinearization method converts the equation into a sequence of linear equations, and then by using the FRC collocation method, these linear equations are solved. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equation by similarity transformations.

Findings

The entropy generation and the effects of the various parameters of the problem are investigated, and various graphs for them are plotted.

Originality/value

Very good approximation solutions to the system of equations in the problem are obtained, and the convergence of numerical results is shown by using plots and tables.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 13 February 2020

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…

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 December 1948

N.A.V. Piercy, L.G. Whitehead and R.A. Tyler

THE greatly increased transition Reynolds numbers now attained in the boundary layers of cylinders having favourably shaped sections have renewed interest in the solution…

Abstract

THE greatly increased transition Reynolds numbers now attained in the boundary layers of cylinders having favourably shaped sections have renewed interest in the solution of the equations of steady flow in a thin boundary layer. It is familiar that the scries solutions of Blasius and Hiemenz, improved by Howarth (ref. 1), and of Falkner (ref. 2) become severely restricted in range when applied to cylinders having other than bluff sections. But it appears that a series solution of substantially greater range is possible, at least for symmetrical flow, provided that the nose of the section is rounded. This problem forms the subject of Section I of the present paper.

Details

Aircraft Engineering and Aerospace Technology, vol. 20 no. 12
Type: Research Article
ISSN: 0002-2667

Article
Publication date: 10 October 2017

Archana M., Gireesha B.J., Prasannakumara B.C. and Rama Subba Reddy Gorla

The effect of non-linear thermal radiation and variable thermo-physical properties are investigated in the Falkner-Skan flow of a Casson nanofluid in the presence of…

Abstract

Purpose

The effect of non-linear thermal radiation and variable thermo-physical properties are investigated in the Falkner-Skan flow of a Casson nanofluid in the presence of magnetic field. The paper aims to discuss this issue.

Design/methodology/approach

Selected bunch of similarity transformations are used to reduce the governing partial differential equations into a set of non-linear ordinary differential equations. The resultant equations are numerically solved using Runge-Kutta-Fehlberg fourth-fifth-order method along with shooting technique.

Findings

The velocity, temperature and concentration profiles are evaluated for several emerging physical parameters and are analyzed through graphs and tables in detail.

Research limitations/implications

This study only begins to reveal the research potential and pitfalls of research and publishing on boundary-layer flow, heat and mass transfer of Casson nanofluid past and the moving and static wedge-shaped bodies.

Originality/value

It is found that the presence of non-linear thermal radiation and variable properties has more influence in heat transfer. Furthermore, temperature profile increases as the radiation parameter increases.

Details

Multidiscipline Modeling in Materials and Structures, vol. 13 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 1 October 1950

V.M. Falkner

1. IN R. & M. 2596 and another report, the I latter concerned mainly with compressibility effects, the writer has considered the aerodynamic loading due to incidence of a…

Abstract

1. IN R. & M. 2596 and another report, the I latter concerned mainly with compressibility effects, the writer has considered the aerodynamic loading due to incidence of a number of wings of varying aspect ratio and sweep‐back. The information given in these reports was obtained by the use of a lattice of vortices for the computation of downwash and by the subsequent determination of the constants in the equation representing the vortex sheet. It is well known that the potential solutions obtained by this simplified representation are not necessarily of more than moderate accuracy when applied to problems in which wing thickness and viscosity are present, and those published have not been carried to a degree sufficient to give accurate detailed pressure distribution in the region of a discontinuity. It has, however, been shown in a later report on the measurement of pressure distribution at the surface of a sweptback wing that the accuracy as regards spanwise load grading and local aerodynamic centre is surprisingly good and it has been thought well worth while to extend the range of information provided in the above reports before proceeding to the more complex task of computing the detailed pressure distribution at the surface of a wing with allowance for viscosity.

Details

Aircraft Engineering and Aerospace Technology, vol. 22 no. 10
Type: Research Article
ISSN: 0002-2667

Article
Publication date: 1 October 1943

Maurice Holt

IN the March issue of AIRCRAFT ENGINEERING Mr. Falkner establishes a new power index law for the skin friction coefficient of a flat plate with fully turbulent boundary layer.

Abstract

IN the March issue of AIRCRAFT ENGINEERING Mr. Falkner establishes a new power index law for the skin friction coefficient of a flat plate with fully turbulent boundary layer.

Details

Aircraft Engineering and Aerospace Technology, vol. 15 no. 10
Type: Research Article
ISSN: 0002-2667

Article
Publication date: 25 February 2014

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

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