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

• Published in: Journal of non-Newtonian fluid mechanics Vol. 102; no. 2; pp. 321 - 342
• Main Authors: Olagunju, David O., Cook, L.Pamela, McKinley, Gareth H.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 15-02-2002; Elsevier
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Linear stability; Non-newtonian fluid flows; Physics; Viscoelastic cone-and-plate flow; Viscous heating; Viscous instability; Viscous heating; Linear stability; Viscoelastic cone-and-plate flow; Viscoelastic fluid; Perturbation theory; Temperature distribution; Shear flow; Oldroyd fluid; Velocity distribution; Cone plate viscosimeter; Viscous dissipation; Axial symmetry
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/S0377-0257(01)00185-9

The effect of viscous heating on the linear stability of torsional flow of 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].