scholarly journals Nano boundary layer equation with nonlinear Navier boundary condition

2007 ◽  
Vol 333 (1) ◽  
pp. 381-400 ◽  
Author(s):  
Miccal T. Matthews ◽  
James M. Hill
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Boundary Layer Equation ◽  
Navier Boundary Condition

scholarly journals Predictor homotopy analysis method (PHAM) for nano boundary layer flows with nonlinear Navier boundary condition: Existence of four solutions

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1687-1697 ◽  
Author(s):  
Elyas Shivanian ◽  
Hamed Alsulami ◽  
Mohammed Alhuthali ◽  
Saeid Abbasbandy
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Homotopy Analysis Method ◽  
Boundary Layer Equation ◽  
Slip Boundary Condition ◽  
Analysis Method ◽  
Slip Boundary ◽  
Navier Boundary Condition ◽  
Homotopy Analysis ◽  
Analytical Series

In the present work, the classical laminar boundary layer equation of the flow away from the origin past a wedge with the no-slip boundary condition replaced by a nonlinear Navier boundary condition is considered. This boundary condition contains an arbitrary index parameter, denoted by n > 0, which appears in the differential equation to be solved. Predictor homotopy analysis method (PHAM) is applied to this problem and more, it is proved corresponding to the value n = 1/3, there exist four solutions. Furthermore, these solutions are approximated by analytical series solution using PHAM for further physical interpretations.

The laminar boundary-layer equation: a method of solution by means of an automatic computer

1955 ◽  
Vol 51 (2) ◽  
pp. 320-332 ◽  
Author(s):  
D. C. F. Leigh
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Iterative Process ◽  
Boundary Layer Equation ◽  
Algebraic Equations ◽  
Automatic Computer ◽  
Linear Algebraic Equations ◽  
Method Of Solution ◽  
Incompressible Boundary

ABSTRACTA method, very suitable for use with an automatic computer, of solving the Hartree-Womersley approximation to the incompressible boundary-layer equation is developed. It is based on an iterative process and the Choleski method of solving a simultaneous set of linear algebraic equations. The programming of this method for an automatic computer is discussed. Tables of a solution of the boundary-layer equation in a region upstream of the separation point are given. In the upstream neighbourhood of separation this solution is compared with Goldstein's asymptotic solution and the agreement is good.

Numerical Study of Boundary Layers With Reverse Wedge Flows Over a Semi-Infinite Flat Plate

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
R. Ahmad ◽  
K. Naeem ◽  
Waqar Ahmed Khan
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Study ◽  
Boundary Layer Equation ◽  
Wedge Angle ◽  
Adverse Pressure Gradient ◽  
Problem Solution ◽  
Weighted Residual Method ◽  
Boundary Layer Problem ◽  
Layer Problem

This paper presents the classical approximation scheme to investigate the velocity profile associated with the Falkner–Skan boundary-layer problem. Solution of the boundary-layer equation is obtained for a model problem in which the flow field contains a substantial region of strongly reversed flow. The problem investigates the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. Optimized results for the dimensionless velocity profiles of reverse wedge flow are presented graphically for different values of wedge angle parameter β taken from 0≤β≤2.5. Weighted residual method (WRM) is used for determining the solution of nonlinear boundary-layer problem. Finally, for β=0 the results of WRM are compared with the results of homotopy perturbation method.

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