Solution of a laminar boundary layer flow via a numerical method

Parand, Kourosh; Shahini, Mehdi; Dehghan, Mehdi

doi:10.1016/j.cnsns.2009.04.007

Cited by 38 publications

(14 citation statements)

References 34 publications

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“…The first problem considered is the classical two-point nonlinear boundary value Blasius problem which models viscous fluid flow over a semi-infinite flat plate. Although solutions for this problem had been obtained as far back as 1908 by Blasius [1], the problem is still of great interest to many researchers as can be seen from the several recent studies [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

“…Owing to the nonlinearity of equations that describe most engineering and science phenomena, many authors traditionally resort to numerical methods such as finite difference methods [12], Runge-Kutta methods [13], finite element methods [14] and spectral methods [4] to solve the governing equations. However, in recent years, several analytical or semi-analytical methods have been proposed and used to find solutions to most nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

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An improved spectral homotopy analysis method for solving boundary layer problems

et al. 2011

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This article presents an improved spectral-homotopy analysis method (ISHAM) for solving nonlinear differential equations. The implementation of this new technique is shown by solving the Falkner-Skan and magnetohydrodynamic boundary layer problems. The results obtained are compared to numerical solutions in the literature and MATLAB's bvp4c solver. The results show that the ISHAM converges faster and gives accurate results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An improved spectral homotopy analysis method for solving boundary layer problems

et al. 2011

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“…It comes with the following boundary conditions: Among them are a host of numerical techniques involving finite differences, finite elements, spectral methods, adomian's polynomials and perturbation methods. A comprehensive list of these can be found in Parand et al [16]. In the calculations reported herein we adopt the shooting technique coupled with the Runge-Kutta ODE numerical solution method as the preferred numerical solution technique for the nonlinear ordinary differential equation.…”

Section: O O Onyejekwe 1429mentioning

confidence: 99%

“…Continuous activity in this area has resulted in a large body of literature. Interested readers can assess a comprehensive list of these contributors in [4] [5].…”

mentioning

confidence: 99%

Incompressible Flow and Heat Transfer over a Plate: A Hybrid Integral Domain-Discretized Numerical Procedure

Onyejekwe¹

2016

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This work deals with incompressible two-dimensional viscous flow over a semi-infinite plate according to the approximations resulting from Prandtl boundary layer theory. The governing nonlinear coupled partial differential equations describing laminar flow are converted to a self-similar type third order ordinary differential equation known as the Falkner-Skan equation. For the purposes of a numerical solution, the Falkner-Skan equation is converted to a system of first order ordinary differential equations. These are numerically addressed by the conventional shooting and bisection methods coupled with the Runge-Kutta technique. However the accompanying energy equation lends itself to a hybrid numerical finite element-boundary integral application. An appropriate complementary differential equation as well as the Green second identity paves the way for the integral representation of the energy equation. This is followed by a finite element-type discretization of the problem domain. Based on the quality of the results obtained herein, a strong case is made for a hybrid numerical scheme as a useful approach for the numerical resolution of boundary layer flows and species transport. Thanks to the sparsity of the resulting coefficient matrix, the solution profiles not only agree with those of similar problems in literature but also are in consonance with the physics they represent.

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“…Using some transformations, the number of researchers extended Chebyshev polynomials to semi-infinite or infinite domains, for example by using x = t−L t+L , L > 0 the rational functions introduced [29,30,31,32,33,34].…”

Section: The Generalized Fractional Order Chebyshev Functionsmentioning

confidence: 99%

Numerical Solution of an Integro-Differential Equation Arising in Oscillating Magnetic Fields

Parand¹,

Delkhosh²

2016

Journal of the Korea Society for Industrial and Applied Mathema

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ABSTRACT. In this paper, an integro-differential equation which arises in oscillating magnetic fields is studied. The generalized fractional order Chebyshev orthogonal functions (GFCF) collocation method used for solving this integral equation. The GFCF collocation method can be used in applied physics, applied mathematics, and engineering applications. The results of applying this procedure to the integro-differential equation with time-periodic coefficients show the high accuracy, simplicity, and efficiency of this method. The present method is converging and the error decreases with increasing collocation points.

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Solution of a laminar boundary layer flow via a numerical method

Cited by 38 publications

References 34 publications

An improved spectral homotopy analysis method for solving boundary layer problems

An improved spectral homotopy analysis method for solving boundary layer problems

Incompressible Flow and Heat Transfer over a Plate: A Hybrid Integral Domain-Discretized Numerical Procedure

Numerical Solution of an Integro-Differential Equation Arising in Oscillating Magnetic Fields

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