Approximate analytical solutions of a class of boundary layer equations over nonlinear stretching surface

Kudenatti, Ramesh B.; Awati, Vishwanath B.; Bujurke, N. M.

doi:10.1016/j.amc.2011.08.049

Cited by 16 publications

(12 citation statements)

References 15 publications

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“…subject to u(0) = 0, u (0) = 1, and u (∞) = 0. This equation represents the study of the two-dimensional laminar flow due to the stretching wall [45][46][47] in the absence of the applied magnetic field. Interestingly, the problem has exact solutions for some values of α.…”

Section: Resultsmentioning

confidence: 99%

Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method

Abdelhakem

Alaa-Eldeen²,

Băleanu

et al. 2021

Fractal Fract

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An efficient technique, called pseudo-Galerkin, is performed to approximate some types of linear/nonlinear BVPs. The core of the performance process is the two well-known weighted residual methods, collocation and Galerkin. A novel basis of functions, consisting of first derivatives of Chebyshev polynomials, has been used. Consequently, new operational matrices for derivatives of any integer order have been introduced. An error analysis is performed to ensure the convergence of the presented method. In addition, the accuracy and the efficiency are verified by solving BVPs examples, including real-life problems.

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Section: Resultsmentioning

confidence: 99%

Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method

Abdelhakem

Alaa-Eldeen²,

Băleanu

et al. 2021

Fractal Fract

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“…In the absence of an applied magnetic field, i.e., M 0 = and general β the problem Eq. (3.6) reduces to the study of a two-dimensional laminar flow due to a stretching wall [10,30,31]. Also, for 0 β = the governing problem describes the well-known Sakiadis problem [32].…”

Section: Resultsmentioning

confidence: 99%

Wavelet-Based Numerical Solution for MHD Boundary-Layer Flow Due to Stretching Sheet

Karkera

Katagi

2021

International Journal of Applied Mechanics and Engineering

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In this paper, a two-dimensional steady flow of a viscous fluid due to a stretching sheet in the presence of a magnetic field is considered. We proposed two new numerical schemes based on the Haar wavelet coupled with a collocation approach and quasi-linearization process for solving the Falkner-Skan equation representing the governing problem. The important derived quantities representing the fluid velocity and wall shear stress for various values of flow parameters M and β are calculated. The proposed methods enable us to obtain the solutions even for negative β, nonlinear stretching parameter, and smaller values of the magnetic parameter (M < 1) which was missing in the earlier findings. Numerical and graphical results obtained show an excellent agreement with the available findings and demonstrate the efficiency and accuracy of the developed schemes. Another significant advantage of the present method is that it does not depends on small parameters and initial presumptions unlike in traditional semi-analytical and numerical methods.

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“…Many researchers have used the Dirichlet series process to solve Stretching sheet type problems due to its widespread application. Kudenatti et al [16] applied the Dirichlet series to investigate a class of boundary layer equations over a nonlinear stretching surface. N Mahesha [19] has proposed a new exponentially decreasing series solution for the coupled nonlinear boundary value problem (BVP).…”

Section: Dirichlet Series Solutionmentioning

confidence: 99%

Approximate Analytical and Numerical Solution of Three-dimensional MHD Flow of an Incompressible Fluid through Porous Media over a Stretching Sheet

Kirsur¹,

Joshi²

2022

Preprint

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The current study focuses on approximate analytical solution of three-dimensional MHD flow of an incompressible fluid through porous media over a stretching sheet using Exponentially decreasing series. The governing equations are transformed into a system of nonlinear ordinary differential equations with boundary conditions using the similarity transformation. It has been attempted to show the reliability and performance of the Dirichlet series in comparison with Direct Numerical Method (DNM). For various flow parameter values, the resulting quantities such as velocity profiles and skin friction coefficient are also geometrically presented.

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Approximate analytical solutions of a class of boundary layer equations over nonlinear stretching surface

Cited by 16 publications

References 15 publications

Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method

Approximating Real-Life BVPs via Chebyshev Polynomials’ First Derivative Pseudo-Galerkin Method

Wavelet-Based Numerical Solution for MHD Boundary-Layer Flow Due to Stretching Sheet

Approximate Analytical and Numerical Solution of Three-dimensional MHD Flow of an Incompressible Fluid through Porous Media over a Stretching Sheet

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