Release:2015, Vol. 1. №2(2)
About the authors:Adelina D. Nizamova, Postgraduate, Institute of Mechanics, Ufa Scientiﬁ c Centre of the Russian Academy of Sciences
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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