Analytic and Numerical Solutions of a Nonlinear Boundary-Layer Problem

1986 ◽  
Vol 75 (1) ◽  
pp. 1-36 ◽  
Author(s):  
Glenn R. Ierley ◽  
Otto G. Ruehr
Keyword(s):  
Boundary Layer ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Boundary Layer Problem ◽  
Layer Problem

scholarly journals Analytic Approximate Solution for Falkner-Skan Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Vasile Marinca ◽  
Remus-Daniel Ene ◽  
Bogdan Marinca
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Rapid Convergence ◽  
Boundary Layer Problem ◽  
Small Parameters ◽  
Optimal Homotopy Asymptotic Method ◽  
Good Agreement ◽  
Layer Problem

This paper deals with the Falkner-Skan nonlinear differential equation. An analytic approximate technique, namely, optimal homotopy asymptotic method (OHAM), is employed to propose a procedure to solve a boundary-layer problem. Our method does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. The obtained results reveal that this procedure is very effective, simple, and accurate. A very good agreement was found between our approximate results and numerical solutions, which prove that OHAM is very efficient in practice, ensuring a very rapid convergence after only one iteration.

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.

On a Boundary Layer Problem

2002 ◽  
Vol 108 (4) ◽  
pp. 369-398 ◽  
Author(s):  
R. Wong ◽  
Heping Yang
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Layer Problem

On Spectral Relaxation Approach to Radiating Powell-Eyring Fluid Flow over a Stretching Disk with Newtonian Heating

2018 ◽  
Vol 387 ◽  
pp. 461-473 ◽  
Author(s):  
K. Gangadhar ◽  
D. Vijaya Kumar ◽  
S. Mohammed Ibrahim ◽  
Oluwole Daniel Makinde
Keyword(s):  
Boundary Layer ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Relaxation Method ◽  
Newtonian Heating ◽  
Nonlinear Boundary Value Problems ◽  
Local Skin ◽  
Boundary Layer Equations ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

In this study we use a new spectral relaxation method to investigate an axisymmetric law laminar boundary layer flow of a viscous incompressible non-Newtonian Eyring-Powell fluid and heat transfer over a heated disk with thermal radiation and Newtonian heating. The transformed boundary layer equations are solved numerically using the spectral relaxation method that has been proposed for the solution of nonlinear boundary layer equations. Numerical solutions are obtained for the local wall temperature, the local skin friction coefficient, as well as the velocity and temperature profiles. We show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to common numerical methods for solving nonlinear boundary value problems. We show that the convergence rate of the spectral relaxation method is significantly improved by using method in conjunction with the successive over-relaxation method. It is observed that CPU time is reduced in SOR method compare with SRM method.

The boundary layer over an impulsively started flat plate

1969 ◽  
Vol 310 (1502) ◽  
pp. 401-414 ◽  
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Surface Shear Stress ◽  
Unsteady State ◽  
Similarity Condition ◽  
Surface Shear ◽  
Boundary Layer Problem ◽  
Independent Variables ◽  
Selection Of ◽  
Layer Problem

A numerical solution has been obtained for the development of the flow from the initial unsteady state described by Rayleigh to the ultimate steady state described by Blasius. The usual formulation of the problem in two independent variables is dropped, and three independent variables, in space and time, are reverted to. The boundary-layer problem is unconventional in that the boundary conditions are not completely known. Instead, it is known that the solution should satisfy a similarity condition, and use is made of this to obtain a solution by iteration. A finite-difference technique of a mixed, explicit-implicit, type is employed. The iteration converges rapidly. It is terminated where the maximum errors are estimated to be about 0.04%. A selection of the results for the velocity profiles and the surface shear stress is presented. One striking feature is the rapidity of the transition from the Rayleigh to the Blasius state. The change is practically complete, at a given station on the plate, by the time the plate has moved a distance equal to four times the distance from the station to the leading edge of the plate.

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