Unsteady MHD Axisymmetric Flow of a Powerlaw Fluid over Radially Stretching Sheet

Abstract

In recent years, the analysis of non-Newtonian fluids has acquired great importance. In industrial and technological applications, non-Newtonian fluids are now acknowledged as more appropriate than Newtonian fluids. The governing equations which arise in case of non-Newtonian fluids are more complicated, of higher order and more non-linear compared to Navier-Stokes equations. In such case, one needs additional boundary conditions for obtaining a unique solution. Rajagopal [1,2] discussed the issue of additional boundary conditions regarding the existence and uniqueness of the solution. Although the flow characteristics of non-Newtonian fluids are more complex, still such fluids are on the leading edge of research in fluid mechanics. The boundary layer flows over a stretching sheet have attracted the attention of many investigators because of their wide applications. Such flows encounter in metal extrusion, metal spinning, continuous stretching of plastic films and artificial fibers, in the manufacture of crystalline materials, polymeric sheets and sheet glass. Sakiadis [3] was probably the first to study the boundary layer flow over a stretched surface moving with a constant velocity. Later on, Crane [4] reported analytical solution of boundary layer flow of an incompressible viscous fluid over a stretching sheet. Schowalter [5] considered the case of the boundary layer flow of non-Newtonian power-law fluid and gave the equations governing the self similar flow of pseudoplastic fluid. Followed by this, many investigators such as Chen and Char [6], Rajagopal [7] and Banks [8] considered the various aspects of the related problem of a stretched sheet with a linear velocity and different thermal boundary conditions. The work on the unsteady boundary layer flows is very scarce in the literature. Much importance has been given to steady flow problems. However, unsteady boundary-layer flows due to an impulsively stretching surface were investigated by some researchers [9-12]. Magnetohydrodynamics (MHD) flow is continuing to be an interesting area of research due to its practical applications in chemical engineering, electrochemistry and polymer processing. Initially, the MHD flows of non-Newtonian fluids were studied by Sarpkaya [13]. The MHD flow over a stretching surface was studied by a number of researchers [14-17]. The work on axisymmetric flow over a radial stretching sheet [18-20] is very scarce in the literature. Motivated by the aforementioned facts, the objective of the present dissertation is therefore to investigate the unsteady MHD axisymmetric flows of power-law fluid over a radially stretching sheet. The entire work in the dissertation has been divided into two chapters. Chapter 1 contains the review of the work by Xu and Liao [21]. In this chapter the analytical solutions for unsteady magnetohydrodynamic flows of non-Newtonian fluids over a stretching plate are constructed. The analytical solutions are obtained by using the homotopy analysis method (HAM) [22-24], which are valid for all values of the dimensionless time. The impact of the emerging flow parameters on the velocity is highlighted and examined graphically. Chapter 2 discusses the unsteady MHD axisymmetric flow of power-law fluid over a radially stretching sheet. The axisymmetric flow equations are reduced by the help of similarity transformations and then solved analytically via homotopy analysis method. Finally, the influence of the emerging flow parameters are plotted and discussed.