Similarity Solutions of Boundary Layer Equations for a Special Non-Newtonian Fluid in a Special Coordinate System

Muhammet Yürüsoy

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Muhammet Yürüsoy. Similarity Solutions of Boundary Layer Equations for a Special Non-Newtonian Fluid in a Special Coordinate System[J]. Applied Mathematics and Mechanics, 2004, 25(5): 535-541.

Citation:

Muhammet Yürüsoy. Similarity Solutions of Boundary Layer Equations for a Special Non-Newtonian Fluid in a Special Coordinate System[J]. Applied Mathematics and Mechanics, 2004, 25(5): 535-541.

Citation:

Muhammet Yürüsoy. Similarity Solutions of Boundary Layer Equations for a Special Non-Newtonian Fluid in a Special Coordinate System[J]. Applied Mathematics and Mechanics, 2004, 25(5): 535-541.

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Similarity Solutions of Boundary Layer Equations for a Special Non-Newtonian Fluid in a Special Coordinate System

Muhammet Yürüsoy

Department of Mechanical Education, Faculty of Technical Education, Ahmet Necdet Sezer Camputs, Afyon Kocatepe University, TR-03200, Afyon, Turkey

Received Date: 2002-10-31
Publish Date: 2004-05-15

Abstract

Abstract

Two dimensional equations of steade motion for third order fluids are expressed in a special coordinate system generated by the potential flow corresponding to an inviscid fluid. For the inviscid flow around an arbitrary object, the streamlines are the phi-coordinates and velocity potential lines are psi-coordinates which form an orthogonal curvilinear set of coordinates. The out come, boundary layer equations, is then shown to be independent of the body shape immersed into the flow. As a first approximation, assumption that second grade terms are negligible compared to viscous and third grade terms. Second grade terms spoil scaling transformation which is only transformation leading to similarity solutions for third grade fluid. By using Lie group methods, infinitesimal generators of boundary layer equations are calculated. The equations are transformed into an ordinary differential system. Numerical solutions of outcoming nonlinear differential equations are found by using combination of a Runge-Kutta algorithm and shooting technique.
- boundary layer equation,
- Lie group,
- third grade fluid

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References(14)

References

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