Asia Pacific Journal of Multidisciplinary Research | Vol. 1, No. 1 | December 2013 _____________________________________________________________________________________________ 51 ISSN 2350 – 7756 www.apjmr.com Numerical solution for the flow over a stretchable disk Sajjad Hussain 1 , Dr. Farooq Ahmad 2 , M. Shafique 3 1 sajjad_h96@yahoo.com, 2 farooqgujar@gmail.com, 3 mshafique6161@hotmail.com 1 Centre for Advanced Studies in Pure and Applied Mathematics, B. Z. Uni., Multan, Pakistan 2 Punjab Higher Education Department, Principal, Govt. Degree College Darya Khan, (Bhakkar) 3 Department of Mathematics, Gomal University, D. I. Khan, PAKISTAN ABSTRACT Numerical solution is obtained for the flow over a stretchable disk with or without rotation. Similarity transformations are used to convert the highly non linear governing partial differential equations to their ordinary differential form. The transformed equations have been solved numerically, using SOR method and Simpson’s (1/3) rule. The numerical results have been improved by Richardson’s extrapolation. The velocity and pressure distributions have been obtained for various values of disk rotation parameter s. When s=0, the flow corresponds to purely stretchable disk and when s>0, the flow is related to a stretching and rotating disk. AMS Subject Classification: 76M20. Keywords: Newtonian fluid, Navier-stokes model, stretchable disk, Similarity transformations, Richardson’s extrapolation. I. INTRODUCTION The fluid flow due to stretchable surface bears important application in extrusion process in plastic and metal industries. Sakiadas [1, 2] examined the boundary layer flow on a continuously stretching surface with a constant speed. Crane [3] obtained a similarity solution in closed analytical form for steady two dimensional incompressible boundary layer flow caused by the stretching of a sheet. Wang [4] studied the fluid flow problem due to stretching boundary for three dimensional case. Chiam [5] investigated steady two dimensional stagnation point flow of an incompressible fluid towards a stretching surface. Mahapatra and Gupta [6, 7] combined both the stagnation point flow and stretching surface. Several researchers including Carragher and Crane [8], Gupta and Gupta [9], Liao and Pop [10] studied different aspects of fluid flow due to moving boundaries. Shafique and Rashid [11] examined the three dimensional fluid motion caused by the stretching of a flat surface. S. Hussain and M. Kamal [12] examined flow of micropolar fluid flow over a stretchable disk. Ever since Von Karman [13] derived the simplified equations that govern the flow over a rotating disk, this problem and many variations of it have attracted several classical text books e.g.[14,15]and researchers. The boundary layer transition and stability of rotating disk flow has been studied by [16, 17]. S. Hussain et al [18] obtained numerical solution of a decelerated rotating disk in a viscous fluid. Fang [19] obtained exact solution for steady state Navier-Stokes