On stability of thermoviscous liquids laminar flow

About the authors:

Adelina D. Nizamova, Postgraduate, Institute of Mechanics, Ufa Scientifi c  Centre of the Russian Academy of Sciences
Victor N. Kireev, Research Associate, Institute of Mechanics, Ufa Scientifi c Centre of the Russian Academy of Sciences, Associate Professor, Cand. Sci. (Phys.-Math.)
Said F. Urmancheev, Dr Sci. (Phys.-Math.) Professor, Mavlutov Institute of Mechanics of RAS, Director

Abstract:

The problem of the influence of temperature dependence of viscosity on stability of laminar liquid flows in a plane channel with non-uniform temperature field is considered. The analytical expressions of undisturbed velocity profi les for plane non-isothermal fluid flows with linear and exponential dependences viscosity on temperature have been derived. The system of two ordinary differential equations for perturbation amplitudes of velocity and temperature has been developed. In the case of isothermal flow, this system of ODE can be reduced to the classical Orr-Sommerfeld equation. The spectra of eigenvalues for laminar flows with different temperature dependences of viscosity have been studied numerically. The considerable differences between the spectra of eigenvalues for the flow of thermoviscous fluid and fluid with constant viscosity are discovered. Consideration of the temperature dependence on fluid viscosity affecting considerably stability of laminar flows is shown.

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