Analysis of Heat and Mass Transfer Effects on Steady Buoyancy Driven Magnetohydrodynamics Fluid Flow Past an Inclined Infinite Flat Plate

Abstract

The phenomenon of natural convection arises in fluids when temperature change causes density variation leading to buoyancy forces acting on the fluid particles. Natural convection flows are frequently encountered in physical and engineering problems such as chemical catalytic reactors, nuclear waste materials, solar collectors, thermal regulation process, security of energy systems etc. When a conductive fluid moves through a magnetic field and an ionized gas is electrically conductive, the fluid may be influenced by the magnetic field. The change in wall temperature causing the free convection flow could be a sudden or a periodic one, leading to a variation in the flow. Such oscillatory flow has applications in industrial and aerospace engineering. However, the temperature and concentration do not remain constant in so many fluid flow problems of practical interests. Moreover, in natural convection flows, thermal input occurs at a surface that , is itself curved or inclined with respect to the direction of gravity field. As a result, we considered a plate at varying, linear temperature distribution to approach such real cases. In pursuit of the objectives of the study, the effects of heat and mass transfer on a two dimensional boundary layer of a steady free convection magnetohydrodynamics (MHD) fluid flow on an. inclined heated plate in which the angle of inclination is varied has been studied. The fluid was taken as viscous, incompressible, electrically conducting. over a heated inclined flat plate. The plate wall and the ambient fluid medium were maintained at constant and different levels of temperature and concentrations such that the heat and mass transfer occurs from plate wall to the fluid medium. Also, due to coupling between the fluid velocity field and thermal/concentration fields, different complex behaviours were expected. To control such processes, we investigated the problem of combined heat and mass transfer permeated by a uniform transverse magnetic field in MHD free convection adjacent to an inclined surface by taking into account effects of viscous dissipation with sinusoidally varying surface temperature on velocity, temperature and concentration. Viscous mechanical dissipation effects are important in geophysical flows and also in certain industrial operations and are usually characterized by the Eckert number. The mathematical formulation yielded a.set of governing partial differential equations (PDEs) lV under a set of appropriate boundary conditions. The PDEs were transformed into ordinary differential equations (ODEs) by some similarity transformation, which were then solved using the shooting iteration technique with the fourth order Runge-Kutta numerical method together with the Secant technique of root finding to determine their solutions. Computations were performed for a wide range of the governing flow parameters and the effects of these flow parameters on the velocity, temperature and concentration shown graphically. From the graphical analysis, it was established that the flow field and other quantities of physical interest are significantly influenced by these parameters. The results of this study of flow over inclined surface is utilized as the basis of many scientific and engineering applications, as the technique of inclination which enhances cooling of materials is significant in industrial processes as cooling of towers, nuclear reactor cooling and metallurgical processes. Finally, employment of an external magnetic field has predominant role in material manufacturing industries as a control mechanism due to generation of Lorentz force.