MHD Slip Flow past a Shrinking Sheet

Santosh Chaudhary,Pradeep Kumar

doi:10.4236/am.2013.43081

Abstract

An analysis is made for the steady two-dimensional laminar boundary layer flow of a viscous, incompressible, electrically conducting fluid near a stagnation point past a shrinking sheet with slip in the presence of a magnetic field. The governing boundary layer equations are transformed to ordinary differential equations by taking suitable similarity variables and solved numerically by Shooting method. The effects of the various parameters such as velocity ratio parameter, slip parameter, Prandtl number, Eckert number and magnetic parameter for velocity and temperature distributions have been discussed in detail through graphical representation.

Highlights

The viscous flow and heat transfer in the boundary layer region due to a stretching sheet has wide theoretical and technical applications in manufacturing process and in industries such as extraction of polymer sheet, paper production, wire drawing, glass-fiber production, the cooling and drying of paper and textiles
It is observed that the velocity boundary layer thickness increases with the increasing values of the velocity ratio parameter c and the slip parameter, whereas a it decreases as the magnetic parameter Rem increases for a fixed
It is observed that for the slip parameter 0.5 the thermal boundary layer thickness decreases with the increasing values of the velocity ratio parameter c, the a Prandtl number Pr and the Eckert number Ec and the reverse phenomenon is observed for the magnetic parameter Rem

Summary

Introduction

The viscous flow and heat transfer in the boundary layer region due to a stretching sheet has wide theoretical and technical applications in manufacturing process and in industries such as extraction of polymer sheet, paper production, wire drawing, glass-fiber production, the cooling and drying of paper and textiles. The effects of heat and mass transfer and magnetic field under various physical conditions have been investigated by several authors such as Chen and Char [2], Chiam [3], Andersson [4], Ariel et al [5], Jat and Chaudhary [6,7], Wang [8], Fang et al [9], Nadeem et al [10], Bhattacharyya and Layek [11] and recently Bhattacharyya et al [12] studied the slip effects on boundary layer stagnation-point flow and heat transfer towards a shrinking sheet. Based on the above mentioned investigations and applications, this paper is concerned with a steady, two dimensional stagnation flow of an electrically conducting fluid past a shrinking sheet in the presence of a magnetic field. The results of velocity and temperature distributions for different parameters such as the velocity ratio parameter, the slip parameter, the Prandtl number, the Eckert number and the magnetic parameter were obtained

Formulation of the Problem

Analysis of the Velocity and the Thermal Boundary Layers

Results and Discussion

Conclusions