Onset of Viscous Dissipation Instability in Plane Couette Flow with Temperature-Dependent Viscosity

Alioune Sene, Sara Ben Sadek, Silvia C. Hirata and Mohamed Najib Ouarzazi ()
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Alioune Sene: Unité de Mécanique de Lille, ULR 7512, Université de Lille, Bd. Paul Langevin, CEDEX, 59655 Villeneuve d’Ascq, France
Sara Ben Sadek: Unité de Mécanique de Lille, ULR 7512, Université de Lille, Bd. Paul Langevin, CEDEX, 59655 Villeneuve d’Ascq, France
Silvia C. Hirata: Unité de Mécanique de Lille, ULR 7512, Université de Lille, Bd. Paul Langevin, CEDEX, 59655 Villeneuve d’Ascq, France
Mohamed Najib Ouarzazi: Unité de Mécanique de Lille, ULR 7512, Université de Lille, Bd. Paul Langevin, CEDEX, 59655 Villeneuve d’Ascq, France

Energies, 2023, vol. 16, issue 10, 1-19

Abstract: The conditions for the onset of dissipation thermal instability with temperature-dependent viscosity in the plane Couette flow of a Newtonian fluid are analyzed. The studied system consists of a horizontal fluid layer confined between an adiabatic (fixed) lower wall and an isothermal (moving) upper wall. Both the exponential and the linear fluidity models are considered in order to account for the thermodependency of the fluid’s viscosity. The linear stability analysis of the base solution with respect to arbitrarily oriented normal modes is carried out numerically by employing a shooting method. The most unstable disturbances are proven to be stationary longitudinal rolls, and their stability is governed by three dimensionless parameters: the viscous dissipation Rayleigh number, Prandtl number and a parameter that represents the variability of the viscosity with temperature. It is shown that the effect of the variation of the viscosity is to promote the stability of the base flow. As expected, the two viscosity models’ results diverge as the variability of the viscosity increases, and the exponential model is found to be more stable than the linear fluidity one. By considering the thermophysical properties of real fluids, it is shown that viscous dissipation thermal instability precedes hydrodynamic instability. An energy budget analysis is proposed to better understand both the stabilization effect of the thermal variability of the viscosity and differences with viscous dissipation hydrodynamic instability.

Keywords: linear stability; Couette flow; viscous heating; temperature-dependent viscosity (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
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