A new numerical approach to MHD flow of a Maxwell fluid past a vertical stretching sheet in the presence of thermophoresis and chemical reaction

Stanford Shateyi

doi:10.1186/1687-2770-2013-196

Abstract

In this study we consider steady MHD flow of a Maxwell fluid past a vertical stretching sheet in a Darcian porous medium. The motion of the fluid is caused by the stretched sheet. The governing boundary layer equations for momentum, thermal energy and concentration are reduced using a similarity transformation to a set of coupled ordinary differential equations. The similarity ordinary differential equations are then solved numerically by a recently developed spectral relaxation method together with the Chebyshev pseudo-spectral collocation method. Effects of the physical parameters on the velocity, temperature and concentration profiles as well as the local skin friction coefficient and the heat and mass transfer rates are depicted graphically and/or in tabular form.MSC: 65Pxx, 76-XX.

Highlights

During the last few years, the boundary layer flows of non-Newtonian fluids driven by stretching surfaces have attracted much research interest [ – ]
The spectral relaxation method (SRM) approach requires that we find the appropriate finite value η∞ which must be selected to be large enough to numerically approximate infinity and the behavior of the governing flow parameters at infinity
In order to select the appropriate value of η, we start with an initial guess, which is relatively small, and solve the governing SRM scheme equations over [, η∞] to obtain the solutions of flow parameters f (η), g(η), θ (η) and φη

Summary

Introduction

During the last few years, the boundary layer flows of non-Newtonian fluids driven by stretching surfaces have attracted much research interest [ – ]. This has been driven by their great importance in engineering and industrial applications. The main difficulty in researching a general boundary-layer theory for non-Newtonian fluids lies, obviously, in the diversity of these fluids, in their constitutive behavior, simultaneous viscous and elastic properties such that differentiating between those effects which arise as a result of a fluid’s shear-dependent viscosity from those which are attributable to the fluid’s elasticity becomes virtually impossible. In some more concentrated polymeric fluids, the Maxwell model is used for large dimensionless relaxation time. It must be noted that the Maxwell fluid model allows for the relaxation effects which cannot be predicted in other different types of non-Newtonian fluids such as second, third and fourth grades

Methods

Results

Conclusion