A mathematical analysis of an isothermal tube drawing process

Abstract

The aim of this paper is to investigate stability of an isothermal glass tube drawing process through control parameters by the method of linear stability analysis. We want to see how the process parameters effect stability of the physical system being considered. For this purpose, we not only prove the existence and uniqueness of the solutions of steady state isothermal tube drawing model but also determine its numerical solution. To perform linear stability analysis, steady state numerical solution is incorporated in the eigenvalue problem, formulated by linearizing the isothermal model. The eigenvalue problem is then solved numerically to determine the critical draw ratio which indicates the onset of instabilities. To the end, stability of the process is analyzed using three different values of space step size. We also observe and discuss the effect of density, viscosity and pressure on stability of the isothermal tube drawing model.

Keywords

• Glass tube drawing process
• Existence and uniqueness
• Linear stability analysis
• Eigenvalue problem
• Critical draw ratio