Stability of Flows due to Stretching Sheets #

Niall Hanevy, Paul Griffiths

14:30 Monday in 4Q08.

Part of the Boundary layer flows and stability session.

Abstract #

Boundary layer flows induced by the extrusion of a surface have received considerable attention since they were first described by Sakiadis [1]. These so-called ‘stretching flows’ are of practical importance to chemical and metallurgy industries where extrusion processes are commonplace. Most previous studies in this area consider the stretching sheet to be solid and free from deformation. Until very recently these types of flows were thought to be linearly stable. However, recent work [2] has shown that these flows are, in fact, linearly unstable to disturbances in the form of Tollmien-Schlichting waves. Our current analysis considers the effect of a large temperature gradient between the surface of the stretching sheet and the stationary flow outside of the boundary layer region. In addition to this, we will also consider the dynamics of a sheet that thins as it is stretched. Our work is motivated by Al-Housseiny & Stone [3] who were the first to consider the isothermal problem. The coupling of the dynamics of the sheet and the induced boundary layer flow imposes restrictions on the validity of self-similar base flow solutions. We will report on the linear stability characteristics of these flows and draw comparisons with previous investigations.

1 Sakiadis, AIChE J 7, 221 (1961). 2 Griffiths et al., Phys. Fluids 33, 084106 (2021). 3 Al-Housseiny and Stone, J. Fluid Mech. 706, 597 (2012).