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

Manisha Patel Manisha Patel,M G Timol,Hema Surati

doi:10.15415/mjis.2021.92004

Abstract

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

Highlights

If the Reynolds number is large, the inertial forces will be predominant and in such a case the effect of viscosity can be considered to be confined in a thin layer known as a velocity boundary layer; adjacent to a solid boundary
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
In the case of fluid motions for which the measured pressure distribution nearly agrees with the perfect fluid theory, such as the flow past the streamlined body or the airfoil, the influence of viscosity at high Reynolds numbers is confined to a very thin layer in the immediate neighborhood of the solid wall

Summary

Introduction

If the Reynolds number is large, the inertial forces will be predominant and in such a case the effect of viscosity can be considered to be confined in a thin layer known as a velocity boundary layer; adjacent to a solid boundary. Which is known as Blasius boundary layer and similarity solution (third order non-linear ODE) is called Blasius equation. Chaotic behavior in the flow along a wedge modeled by the Blasius equation along with the numerical solutions was discussed by Basu et al (2011). Another class of boundary layer problem for a stretching sheet relevant to the Blasius equation was studied by Sakiadis (1961). The generalized Blasius equations was discussed by Benlahsen et al (2008) They considered the non-linear relationship for the strees and rate of deformation, the non-Newtonian case, in the Blasius boundary layer. It can be applied to some other real world problems

Blasius Boundary Layer with Power-Law Fluid Model

Blasius Boundary Layer with Sisko Fluid Model

Blasius Boundary Layer with Prandtl Fluid Model

Results and Discussions

Conclusion