Chebyshev finite difference method for heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation

Abstract

Numerical solutions are obtained for the problem which involves both the heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching surface with Ohmic heating and viscous dissipation using Chebyshev finite difference method (ChFD). A similarity transformation was employed to change the governing momentum, angular momentum, energy, and concentration partial differential equations into ordinary ones. Numerical calculations have been carried out for various values of magnetic field parameter, material parameter, Prandtl number, Eckert number, Schmidt number, couple stress at the surface, local Nusselt number and Sherwood number. The numerical results indicate that the temperature and the concentration increase, while the velocities, the Nusselt number and the Sherwood number decrease with increasing magnetic field parameter. In all of the above results, the material parameter has the opposite effect of magnetic field parameter. The temperature increases with increasing Eckert number, and decreases with increasing Prandtl number. An increase in the Schmidt number gives an increase in the Sherwood number, or a decrease in the concentration.

Introduction

Flow, heat, and mass transport phenomena over a continuous, moving flat surface are important in a number of technological processes. The analysis of such transport phenomena finds applications in different areas such as the aerodynamic extrusion of plastic sheets, the continuous casting, rolling, and extrusion in manufacturing processes, and the boundary layer along a liquid film in condensation processes. Erickson et al. [13] studied the problem of heat and mass transfer in the laminar boundary layer flow of moving flat surface with constant surface velocity and temperature, focusing on the effect of suction/injection. The problem of heat and mass transfer on a stretching sheet with suction or blowing was investigated by Gupta and Gupta [18]. Recently, some researchers have been led to include various physical aspects of the problem of combined heat and mass transfer [1], [5], [9]. All of the above investigators, however, restrict their analysis to the Newtonian fluid flow.

A new stage in the evaluation of fluid dynamic theory is in progress because of its increasing importance in processing industries and elsewhere of materials whose behaviour in shear cannot be characterized by Newtonian relationships.

The theory of micropolar fluids proposed by Eringen [14], [15] deals with a class of fluids which exhibit certain microscopic effects arising from local structure micromotions of the fluid elements. Physical micropolar fluids may present the non-Newtonian fluid models which can be used to analyze the behaviour of exotic lubricants [22], [23], colloidal suspensions or polymeric fluids [21], liquid crystals [24], [25] and animal blood [3]. Hassanien [19] investigated boundary layer flow and heat transfer on continuous accelerated sheet extruded in ambient micropolar fluid. The numerical solution for heat transfer in a micropolar fluid over a stretching sheet has been studied also by Hassanien and Gorla [20]. The present problem finds applications in magnetohydrodynamic (MHD) generators with neutral fluid seeding in the form of rigid microinclusions. Also, many industrial applications involve fluids as a working medium; and in such applications unclean fluids (i.e., clean fluid + interspersed particles). Recently, Eldabe et al. [10] studied numerically the problem of heat transfer to MHD flow of a micropolar fluid from a stretching sheet with suction and blowing through a porous medium by using Chebyshev finite difference method (ChFD).

However, all of the above mentioned researches dealing with the micropolar fluids concentrate only on the heat transfer problem. None of them deals with the more complicated problem which involves both the heat and mass transfer in the electrically conducting fluid. Along this attitude of research, Eldabe and Mohamed [11] studied the problem of heat and mass transfer in hydromagnetic flow of the non-Newtonian fluid with heat source over an accelerating surface through a porous medium. Also, Eldabe et al. [12] studied numerically the problem of thermal-diffusion and diffusion-thermo effects on mixed free-forced convection and mass transfer boundary layer flow for non-Newtonian fluid with temperature dependent viscosity by using ChFD method.

As a result, this research attempts to solve this more complicated problem and investigate, by using the micropolar approach, the effects of magnetic field on the heat and mass transfer characteristics from the continuous flat surface moving in a quiescent electrically conducting fluid. In this work the two-dimensional continuity, momentum, angular momentum, energy, and concentration equations have been reduced to a system of nonlinear ordinary differential equations, which are solved numerically by using Chebyshev finite difference method (ChFD). The effects of different parameters of the problem on the flow, heat and mass transfer have been shown in tables and graphically.