Numerical Solution for Accelerated Rotating Disk in a Viscous Fluid

Affiliation(s)

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

Punjab Higher Education Department, Govt. Degree College Darya Khan, Bhakkar, Pakistan.

Department of Mathematics, Gomal University, Dera Ismail Khan, Pakistan.

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

Punjab Higher Education Department, Govt. Degree College Darya Khan, Bhakkar, Pakistan.

Department of Mathematics, Gomal University, Dera Ismail Khan, Pakistan.

Abstract

The problem of a disk rotating in a viscous fluid has been investigated. The disk is accelerated with angular velocity proportional to time. Employing suitable similarity transformations the governing partial differential equations are transformed in to ordinary differential form. The resulting equations are solved numerically using SOR method and Simpson’s (1/3) rule. The results have been improved by using Richardson’s extrapolation. The effect of the non-dimensional parameter s which measures unsteadiness is observed on velocity components, skin friction coefficient and torque of the disk.

The problem of a disk rotating in a viscous fluid has been investigated. The disk is accelerated with angular velocity proportional to time. Employing suitable similarity transformations the governing partial differential equations are transformed in to ordinary differential form. The resulting equations are solved numerically using SOR method and Simpson’s (1/3) rule. The results have been improved by using Richardson’s extrapolation. The effect of the non-dimensional parameter s which measures unsteadiness is observed on velocity components, skin friction coefficient and torque of the disk.

Cite this paper

S. Hussain, F. Ahmad, M. Shafique and S. Hussain, "Numerical Solution for Accelerated Rotating Disk in a Viscous Fluid,"*Applied Mathematics*, Vol. 4 No. 6, 2013, pp. 899-902. doi: 10.4236/am.2013.46124.

S. Hussain, F. Ahmad, M. Shafique and S. Hussain, "Numerical Solution for Accelerated Rotating Disk in a Viscous Fluid,"

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