scholarly journals Extension of Blasius Newtonian Boundary Layer to Blasius Non-Newtonian Boundary Layer

2021 ◽  
Vol 9 (2) ◽  
pp. 35-41
Author(s):  
Manisha Patel ◽  
Hema Surati ◽  
M G Timol
Keyword(s):  
Boundary Layer ◽  
Similarity Solutions ◽  
Power Law Model ◽  
Prandtl Model ◽  
Blasius Boundary Layer ◽  
Blasius Equation ◽  
Boundary Layer Problems ◽  
The One ◽  
Graphical Presentation ◽  
Theory Technique

Blasius equation is very well known and it aries in many boundary layer problems of fluid dynamics. In this present article, the Blasius boundary layer is extended by transforming the stress strain term from Newtonian to non-Newtonian. The extension of Blasius boundary layer is discussed using some non-newtonian fluid models like, Power-law model, Sisko model and Prandtl model. The Generalised governing partial differential equations for Blasius boundary layer for all above three models are transformed into the non-linear ordinary differewntial equations using the one parameter deductive group theory technique. The obtained similarity solutions are then solved numerically. The graphical presentation is also explained for the same. It concludes that velocity increases more rapidly when fluid index is moving from shear thickninhg to shear thininhg fluid.MSC 2020 No.: 76A05, 76D10, 76M99

A New Approach for the Derivation of the Similarity Equation of the 2-D Unsteady Boundary Layer Equations

2012 ◽  
Author(s):  
Md. Abdus Sattar
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Similarity Solutions ◽  
Length Scale ◽  
Local Similarity ◽  
Unsteady Boundary Layer ◽  
Similarity Equation ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
The One

A local similarity equation for the hydrodynamic 2-D unsteady boundary layer equations has been derived based on a time dependent length scale initially introduced by the author in solving several unsteady one-dimensional boundary layer problems. Similarity conditions for the potential flow velocity distribution are also derived. This derivation shows that local similarity solutions exist only when the potential velocity is inversely proportional to a power of the length scale mentioned above and is directly proportional to a power of the length measured along the boundary. For a particular case of a flat plate the derived similarity equation exactly corresponds to the one obtained by Ma and Hui[1]. Numerical solutions to the above similarity equation are also obtained and displayed graphically.

scholarly journals Solving Prandtl-Blasius boundary layer equation using Maple

2020 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Boundary Layer ◽  
Analytic Solution ◽  
Boundary Layer Equation ◽  
Approximate Analytic Solution ◽  
Convergence Radius ◽  
Classic Problem ◽  
Runge Kutta Method ◽  
Blasius Boundary Layer ◽  
Blasius Equation ◽  
Maple Code

A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple code as its numerical solution. The solutions were obtained from the Maple code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting.

scholarly journals Solving Prandtl-Blasius Boundary Layer Equation Using Maple

2020 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Boundary Layer ◽  
Analytic Solution ◽  
Boundary Layer Equation ◽  
Approximate Analytic Solution ◽  
Convergence Radius ◽  
Classic Problem ◽  
Runge Kutta Method ◽  
Blasius Boundary Layer ◽  
Blasius Equation ◽  
Maple Code

A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple code as its numerical solution. The solutions were obtained from the Maple code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting. Similarly, the study resolves some boundary layer related problems and provide relevant Maple codes for these.

Acoustic receptivity and evolution of two-dimensional and oblique disturbances in a Blasius boundary layer

2001 ◽  
Vol 432 ◽  
pp. 69-90 ◽  
Author(s):  
RUDOLPH A. KING ◽  
KENNETH S. BREUER
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Acoustic Wave ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Surface Waviness ◽  
S Wave ◽  
Boundary Layer Instability ◽  
Blasius Boundary Layer ◽  
Tollmien Schlichting

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional and oblique (three-dimensional) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well-defined wavenumber spectrum with fundamental wavenumber kw. A planar downstream-travelling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to kts = kw. The range of acoustic forcing levels, ε, and roughness heights, Δh, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination εΔh resulted in subsequent nonlinear development of the Tollmien–Schlichting (T–S) wave. This study provides the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the two-dimensional and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T–S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.

An Initial Value Method for the Solution of a Class of Nonlinear Equations in Fluid Mechanics

1970 ◽  
Vol 92 (3) ◽  
pp. 503-508 ◽  
Author(s):  
T. Y. Na
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Porous Medium ◽  
Fluid Mechanics ◽  
Boundary Layer Equation ◽  
Physical Parameters ◽  
Point Boundary ◽  
Trial And Error ◽  
Initial Value ◽  
Blasius Boundary Layer

An initial value method is introduced in this paper for the solution of a class of nonlinear two-point boundary value problems. The method can be applied to the class of equations where certain physical parameters appear either in the differential equation or in the boundary conditions or both. Application of this method to two problems in Fluid Mechanics, namely, Blasius’ boundary layer equation with suction (or blowing) and/or slip and the unsteady flow of a gas through a porous medium, are presented as illustrations of this method. The trial-and-error process usually required for the solution of such equations is eliminated.

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