Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls

2000 ◽  
Vol 19 (1) ◽  
pp. 109-122 ◽  
Author(s):  
Eugen Magyari ◽  
Bruno Keller
Keyword(s):  
Boundary Layer ◽  
Exact Solutions ◽  
Boundary Layer Flows ◽  
Self Similar

scholarly journals Some Exact Solutions of Boundary Layer Flows along a Vertical Plate with Buoyancy Forces Combined with Lorentz Forces under Uniform Suction

2008 ◽  
Vol 2008 ◽  
pp. 1-18 ◽  
Author(s):  
Asterios Pantokratoras
Keyword(s):  
Boundary Layer ◽  
Exact Solutions ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Porous Plate ◽  
Boundary Layer Flows ◽  
Flow Separation Control ◽  
Uniform Suction ◽  
Buoyancy Forces ◽  
Lorentz Forces

Exact analytical solutions of boundary layer flows along a vertical porous plate with uniform suction are derived and presented in this paper. The solutions concern the Blasius, Sakiadis, and Blasius-Sakiadis flows with buoyancy forces combined with either MHD Lorentz or EMHD Lorentz forces. In addition, some exact solutions are presented specifically for water in the temperature range of , where water density is nearly parabolic. Except for their use as benchmarking means for testing the numerical solution of the Navier-Stokes equations, the presented exact solutions with EMHD forces have use in flow separation control in aeronautics and hydronautics, whereas the MHD results have applications in process metallurgy and fusion technology. These analytical solutions are valid for flows with strong suction.

Galerkin-Laguerre Spectral Solution of Self-Similar Boundary Layer Problems

2012 ◽  
Vol 12 (5) ◽  
pp. 1329-1358 ◽  
Author(s):  
F. Auteri ◽  
L. Quartapelle
Keyword(s):  
Boundary Layer ◽  
Separated Flows ◽  
Spectral Approximation ◽  
Boundary Layer Flows ◽  
Spectral Solution ◽  
Solution Algorithms ◽  
Laguerre Basis ◽  
Special Basis ◽  
Self Similar ◽  
Sommerfeld Equation

AbstractIn this work the Laguerre basis for the biharmonic equation introduced by Jie Shen is employed in the spectral solution of self-similar problems of the boundary layer theory. An original Petrov-Galerkin formulation of the Falkner-Skan equation is presented which is based on a judiciously chosen special basis function to capture the asymptotic behaviour of the unknown. A spectral method of remarkable simplicity is obtained for computing Falkner-Skan-Cooke boundary layer flows. The accuracy and efficiency of the Laguerre spectral approximation is illustrated by determining the linear stability of nonseparated and separated flows according to the Orr-Sommerfeld equation. The pentadiagonal matrices representing the derivative operators are explicitly provided in an Appendix to aid an immediate implementation of the spectral solution algorithms.

On boundary-layer flows induced by the motion of stretching surfaces

2012 ◽  
Vol 706 ◽  
pp. 597-606 ◽  
Author(s):  
Talal T. Al-Housseiny ◽  
Howard A. Stone
Keyword(s):  
Boundary Layer ◽  
Newtonian Fluid ◽  
Laminar Boundary Layer ◽  
Linear Elasticity ◽  
Classical Problem ◽  
Boundary Layer Flows ◽  
Elastic Sheet ◽  
Stretching Surfaces ◽  
Self Similar ◽  
Similar Solutions

AbstractWe investigate laminar boundary-layer flows due to translating, stretching, incompressible sheets. Unlike the classical problem in the literature where the mechanics of the sheet are neglected, and kinematics are prescribed, the dynamics of both the fluid and the sheet are herein coupled. Two types of stretching sheets are considered: an elastic sheet that obeys linear elasticity and a sheet that deforms as a viscous Newtonian fluid. In both cases, we find self-similar solutions to the coupled fluid/sheet system. These self-similar solutions are only valid under limiting conditions.

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