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

Author(s)
Sajjad Hussain,
Muhammad Anwar Kamal,
Farooq Ahmad,
Muhammad Ali,
Muhammad Shafique,
Sifat Hussain

Affiliation(s)

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.

Department of Mathematics, King Suleman Bin Abdulaziz University, Al-Kharj, Saudi Arabia.

Department of Mathematics, Minhaj University, Lahore, Pakistan.

Department of Mathematics, Gomal University, D. I. Khan, Pakistan.

Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan.

Department of Mathematics, King Suleman Bin Abdulaziz University, Al-Kharj, Saudi Arabia.

Department of Mathematics, Minhaj University, Lahore, Pakistan.

Department of Mathematics, Gomal University, D. I. Khan, Pakistan.

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.

Cite this paper

S. Hussain, M. Kamal, F. Ahmad, M. Ali, M. Shafique and S. Hussain, "Numerical Solution for a Similar Flow between Two Disks in the Presence of a Magnetic Field,"*Applied Mathematics*, Vol. 4 No. 8, 2013, pp. 1163-1167. doi: 10.4236/am.2013.48155.

S. Hussain, M. Kamal, F. Ahmad, M. Ali, M. Shafique and S. Hussain, "Numerical Solution for a Similar Flow between Two Disks in the Presence of a Magnetic Field,"

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