Similarity treatment for MHD free convective boundary layer flow of a class of non-Newtonian fluids

Rajesh Darji,Munir Timol

doi:10.5937/fmet1602197d

Abstract

Deductive group symmetry treatment is applied to derive the similarity transformations for the free convective boundary layer flow of a class of non-Newtonian fluids past over a two-dimensional surface and flowing under the influence of transverse magnetic field. Numerical solutions are obtained for particular Non-Newtonian fluid model namely Prandtl Eyring fluid, in a graphical form . The important physical quantities like velocity distribution, skin friction coefficient and temperature variations are discussed.

Highlights

The classical theory of fluid mechanics is based upon the hypothesis of a linear relationship between two tensor components, shearing stress and rate of strain as, τ = −μ ∂u (1) ∂ yThe fluids with properties different from that described by equation (1), called Non-Newtonian fluids.Flow of Non-Newtonian fluids has attained a great success in the theory of fluid mechanics due to its applications in biological sciences and industry
In present work we concentrate our discussion on the similarity solution of steady laminar natural convection flows of generalized Non-Newtonian fluid
We investigate the MHD boundary layer flow of a class of Non-Newtonian fluids characterized by the property that its stress tensor component τij can be related to the strain rate component eij by the arbitrary continuous function of the type

Summary

INTRODUCTION

In present work we concentrate our discussion on the similarity solution of steady laminar natural convection flows of generalized Non-Newtonian fluid. Such a class of fluids are severely omitted in the analysis due to mathematical complicity of its nonlinear stress-strain relationship. From these charts, we noticed that all the similarity solutions presented there in are derived either by adopting or by ad-hoc assumption on similarity variables. This method has been successfully applied to various non-linear problems by Abd-el-Malek et al [21], Adnan et al [22], Darji and Timol [23, 24]

GOVERNING EQUATIONS

SIMILARITY ANALYSIS

PRANDTL EYRING FLUID MODEL

RESULTS

CONCLUSION