The Solution of a Coupled Nonlinear System Arising in a Three-Dimensional Rotating Flow Using Spline Method

The behavior of the non-linear-coupled systems arising in axially symmetric hydromagnetics flow between two horizontal plates in a rotating system is analyzed, where the lower is a stretching sheet and upper is a porous solid plate. The equations of conservation of mass and momentum are transformed to a system of coupled nonlinear ordinary differential equations. These equations for the velocity field are solved numerically by using quintic spline collocation method. To solve the nonlinear equation, quasilinearization technique has been used. The numerical results are presented through graphs, in which the effects of viscosity, through flow, magnetic flux, and rotational velocity on velocity field are discussed. 1. Introduction In fluid mechanics, the problems associated with the flow that occurs due to the rotation of a single disk or that between two rotating disks have been found of interest of many researchers. Flows between finite disks were studied by Dijkstra and van Heijst [1], Adams and Szeri [2] and Szeri et al. [3]. Berker [4] showed that when the two disks are rotating with the same angular speed, there exists a one parameter family of solutions all but one of which is not rotationally symmetric. This result has been extended by Parter and Rajagopal [5], to disks rotating with differing angular speeds; they prove that the rotationally symmetric solutions are never isolated when considered within the full scope of the Navier-Stokes equations. The numerical study of the asymmetric flow has been carried out by Lai et al. [6, 7]. Recently, hydromagnetic flow and heat transfer problems have become more important industrially. In view of these, Chakrabarti and Gupta [8] studied the hydromagnetic flow and heat transfer in a fluid, initially at rest and at uniform temperature, over a stretching sheet at a different uniform temperature. Banerjee [9] studied the effect of rotation on the hydromagnetic flow between two parallel plates where the upper plate is porous and solid, and the lower plate is a stretching sheet. In this paper, we analyze the behavior of the solution of the nonlinear coupled systems arising in axially symmetric hydromagnetic flow between two horizontal plates in a rotating system, where the lower plate is a stretching sheet. The governing coupled ordinary differential equations are solved by quintic spline collocation method. In Section 2, the mathematical model of the problem given by Vajravelu and Kumar [10] is presented. The quintic spline collocation method is explained in Section 3. The results are displayed in graphical