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

Third order nonlinear ordinary differential equations, subject to appropriate boundary conditions arising in fluid dynamics, are solved using three different methods viz., the Dirichlet series, method of stretching of variables, and asymptotic function method. Similarity transformations are used to...

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Bibliographic Details
Published in:Applied mathematics and computation 2011-11, Vol.218 (6), p.2952-2959
Main Authors: Kudenatti, Ramesh B., Awati, Vishwanath B., Bujurke, N.M.
Format: Article
Language:English
Subjects:
Asymptotic method
Asymptotic properties
Boundary layer equations
Differential equations
Dirichlet problem
Dirichlet series
Mathematical analysis
Mathematical models
Nonlinearity
Skin friction
Stretching
Stretching of variables
Stretching surface
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Summary:Third order nonlinear ordinary differential equations, subject to appropriate boundary conditions arising in fluid dynamics, are solved using three different methods viz., the Dirichlet series, method of stretching of variables, and asymptotic function method. Similarity transformations are used to convert the governing partial differential equations into nonlinear ordinary differential equations. The numerical results obtained from the above methods for various problems are given in terms of skin friction. Our study revealed that the results obtained from these methods agree well with those of direct numerical simulation of ordinary differential equations. Also, these methods have advantages over pure numerical methods in obtaining derived quantities such as velocity profile accurately for various values of the parameters at a stretch.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2011.08.049