Numerical Solution of MHD Flow of Micropolar Fluid with Heat and Mass Transfer towards a Stagnation Point on a Vertical Plate

N T El-Dabe,R R Rizkallah,A S Al-Bareda,K M Ewis,A Y Ghaly

doi:10.4236/ajcm.2015.52013

Abstract

The paper investigates the numerical solution of problem of magnetohydrodynamic (MHD) micropolar fluid flow with heat and mass transfer towards a stagnation point on a vertical plate. In this study, we consider both strong concentrations (n = 0) and weak concentrations (n = 1/2). The governing equations have been transformed into nonlinear ordinary differential equations by applying the similarity transformation and have been solved numerically by using the finite difference method (FDM) and analytically by using (DTM). The effects of various governing parameters, namely, material parameter, radiation parameter, magnetic parameter, Prandtl number, Schmidt number, chemical reaction parameter and Soret number on the velocity, microrotation, temperature and concentration have been computed and discussed in detail through some figures and tables. In order to verify the accuracy of the present results, we have compared these results with the analytical solutions by using the differential transform method (DTM) and the multi-step differential transform method (MDTM). It is observed that this approximate numerical solution is in good agreement with the analytical solution.

Highlights

Finite Difference Method (FDM), Differential Transform Method (DTM), Micropolar Fluid, MHD, Heat and Mass Transfer, Stagnation Flow, Chemical Reaction, Radiation
Devi et al extended the problem posed by Ramachandran et al [10] to the unsteady case, and they found that dual solution exists for a certain range of the buoyancy parameter when the flow is opposing
Olanrewaju and Adesanya [20] studied the effects of radiation and viscous dissipation on stagnation flow of a micropolar fluid towards a vertical permeable surface

Summary

Introduction

Finite Difference Method (FDM), Differential Transform Method (DTM), Micropolar Fluid, MHD, Heat and Mass Transfer, Stagnation Flow, Chemical Reaction, Radiation. Ishak et al [8] investigated the steady two-dimensional stagnation point flow of an incompressible micropolar fluid towards a vertical stretching sheet. Manjoolatha et al [21] studied the radiation and mass transfer effects on MHD flow of a micropolar fluid towards a stagnation point on a vertical stretching sheet. The main objective of the present work is to study the numerical solutions of problem of magnetohydrodynamic (MHD) micropolar fluid flow with heat and mass transfer towards a stagnation point on a vertical plate. The magnetic Reynolds number of the flow is taken to be small enough so that the induced magnetic field is negligible

Objectives

Methods

Results

Conclusion