J. Non-Newtonian Fluid Mech. 102 (2002) 321–342

Effect of viscous heating on linear stability of viscoelastic cone-and-plate flow: axisymmetric case

David O. Olagunju (1),L. Pamela Cook (1), Gareth H. McKinley (2)

(1)Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA
(2)Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA


The effect of viscous heating on the linear stability of torsional flowof a viscoelastic fluid is analyzed.We consider an Oldroyd-B fluid subjected to a steady shearing motion in a cone–plate system with small gap. Previous experimental and analytical results show that in the isothermal case the flow is unstable to short wavelength disturbances for values of the Deborah number greater than some critical value. In this paper we show that viscous heating, which is characterized by a radially averaged Nahme number, Na, has a stabilizing effect on both long wave and short wave disturbances. This is in qualitative agreement with experimental results of Rothstein and McKinley [Phys. Fluids 13 (2001) 382]. © 2002 Elsevier Science B.V. All rights reserved.