On a nonisothermal stability problem for a viscous fluid flow in a plane channel

Abstract

The paper considers the influence of the nature of the change in the dependence of viscosity on temperature on the stability of the flow of a 45 % aqueous solution of propylene glycol in a flat channel with a linear temperature distribution. The solution of the hydrodynamic stability problem was reduced to the determination of the spectra of the generalized Orr – Sommerfeld equation. Spectra of eigenvalues and eigenfunctions were constructed for both sections of the dependence of viscosity on temperature, the corresponding critical Reynolds numbers were determined. The results of the study indicate that the laminar-turbulent transition depends not only on the presence of a dependence of viscosity on temperature, but also on the intensity of its change.