Numerical Solution for a Similar Flow between Two Disks in the Presence of a Magnetic Field

Abstract

Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H (1－αt) 1/2 and a magnetic field proportional to B 0 (1－αt) -1/2 is applied perpendicular to the disks where H denotes a representative length, B O denotes a representative magnetic field and α -1 denotes a representative time. Similarity transformations are used to convert the governing partial differential equations of motion in to ordinary differential form. The resulting ordinary differential equations are solved numerically using SOR method, Richardson extrapolation and Simpson’s (1/3) Rule. Our numerical scheme is straightforward, efficient and easy to program.