Relevant bibliographies by topics / Falkner-Skan

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Academic literature on the topic 'Falkner-Skan'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 February 2022

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Journal articles on the topic "Falkner-Skan"

1

Calvert, Velinda, and Mohsen Razzaghi. "Solutions of the Blasius and MHD Falkner-Skan boundary-layer equations by modified rational Bernoulli functions." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 8 (2017): 1687–705. http://dx.doi.org/10.1108/hff-05-2016-0190.

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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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2

Awais, Muhammad, A. Aqsa, Saeed Awan, Saeed Rehman, and Muhammad Raja. "Hydromagnetic Falkner-Skan fluid rheology with heat transfer properties." Thermal Science 24, no. 1 Part A (2020): 339–46. http://dx.doi.org/10.2298/tsci180509312a.

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This article addresses the effects of heat transfer on magnetohydrodynamic Falkner-Skan wedge flow of a Jeffery fluid. The continuity, momentum and energy balance equations yield the relevant PDE which are transforms to ODE by exploitation of similarity variables. Strength of optimal homotopy series solutions is practiced to solved analytically the transformed ODE model of hydromagnetic Falkner-Skan fluid rheology with heat transfer scenarios. The graphical and numerical illustrations of the result are presented for different interesting flow parameters. Numerical values of Nusselt number are tabulated. It is observed that for the Falkner-Skan rheology, the applied magnetic field acts as a controlling agnet which controls the fluids velocity up to the desired value whereas Debrorah number enhances the fluid velocity.
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3

Lan, K. Q., and G. C. Yang. "Positive Solutions of the Falkner–Skan Equation Arising in the Boundary Layer Theory." Canadian Mathematical Bulletin 51, no. 3 (2008): 386–98. http://dx.doi.org/10.4153/cmb-2008-039-7.

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AbstractThe well-known Falkner–Skan equation is one of the most important equations in laminar boundary layer theory and is used to describe the steady two-dimensional flow of a slightly viscous incompressible fluid past wedge shaped bodies of angles related to λπ/2, where λ ∈ ℝ is a parameter involved in the equation. It is known that there exists λ* < 0 such that the equation with suitable boundary conditions has at least one positive solution for each λ ≥ λ* and has no positive solutions for λ < λ*. The known numerical result shows λ* = –0.1988. In this paper, λ* ∈ [–0.4,–0.12] is proved analytically by establishing a singular integral equation which is equivalent to the Falkner–Skan equation. The equivalence result provides new techniques to study properties and existence of solutions of the Falkner–Skan equation.
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4

Eerdun, Buhe, Qiqige Eerdun, Bala Huhe, Chaolu Temuer, and Jing-Yu Wang. "Variational iteration method with He's polynomials for MHD Falkner-Skan flow over permeable wall based on Lie symmetry method." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 6 (2014): 1348–62. http://dx.doi.org/10.1108/hff-02-2013-0072.

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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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5

Jiwari, Ram, Vikas Kumar, Ram Karan, and Ali Saleh Alshomrani. "Haar wavelet quasilinearization approach for MHD Falkner–Skan flow over permeable wall via Lie group method." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 6 (2017): 1332–50. http://dx.doi.org/10.1108/hff-04-2016-0145.

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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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6

Ullah, H., S. Islam, M. Idrees, and M. Arif. "Solution of Boundary Layer Problems with Heat Transfer by Optimal Homotopy Asymptotic Method." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/324869.

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Application of Optimal Homotopy Asymptotic Method (OHAM), a new analytic approximate technique for treatment of Falkner-Skan equations with heat transfer, has been applied in this work. To see the efficiency of the method, we consider Falkner-Skan equations with heat transfer. It provides us with a convenient way to control the convergence of approximate solutions when it is compared with other methods of solution found in the literature as finite difference (N. S. Asaithambi, 1997) and shooting method (Cebeci and Keller, 1971). The obtained solutions show that OHAM is effective, simpler, easier, and explicit.
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7

Belden, E. R., Z. A. Dickman, S. J. Weinstein, A. D. Archibee, E. Burroughs, and N. S. Barlow. "Asymptotic Approximant for the Falkner–Skan Boundary Layer Equation." Quarterly Journal of Mechanics and Applied Mathematics 73, no. 1 (2020): 36–50. http://dx.doi.org/10.1093/qjmam/hbz021.

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Summary We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., Q. J. Mech. Appl. Math. 70 (2017) 21–48.) yields accurate analytic closed-form solutions to the Falkner–Skan boundary layer equation for flow over a wedge having angle $\beta\pi/2$ to the horizontal. A wide range of wedge angles satisfying $\beta\in[-0.198837735, 1]$ are considered, and the previously established non-unique solutions for $\beta<0$ having positive and negative shear rates along the wedge are accurately represented. The approximant is used to determine the singularities in the complex plane that prescribe the radius of convergence of the power series solution to the Falkner–Skan equation. An attractive feature of the approximant is that it may be constructed quickly by recursion compared with traditional Padé approximants that require a matrix inversion. The accuracy of the approximant is verified by numerical solutions, and benchmark numerical values are obtained that characterize the asymptotic behavior of the Falkner–Skan solution at large distances from the wedge.
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8

Asaithambi, Asai. "A series solution of the Falkner–Skan equation using the crocco–wang transformation." International Journal of Modern Physics C 28, no. 11 (2017): 1750139. http://dx.doi.org/10.1142/s012918311750139x.

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A direct series solution for the Falkner–Skan equation is obtained by first transforming the problem using the Crocco–Wang transformation. The transformation converts the third-order problem to a second-order two-point boundary value problem. The method first constructs a series involving the unknown skin-friction coefficient [Formula: see text]. Then, [Formula: see text] is determined by using the secant method or Newton’s method. The derivative needed for Newton’s method is also computed using a series derived from the transformed differential equation. The method is validated by solving the Falkner–Skan equation for several cases reported previously in the literature.
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9

Hendi, Fatheah A., and Majid Hussain. "Analytic Solution for MHD Falkner-Skan Flow over a Porous Surface." Journal of Applied Mathematics 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/123185.

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10

Afzal, Noor. "Improved series solutions of Falkner-Skan equation." AIAA Journal 23, no. 6 (1985): 969–71. http://dx.doi.org/10.2514/3.9020.

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