Variation in the region of hydrodynаmic stаbility depending on a thermoviscosity pаrаmeter

This paper considers an incompressible fluid flow in а flat channel with а nonuniform temperature field under the pressure drop. The diagrams of the increase in the intensity of disturbances for the first eigenvalue and the decay of disturbances for the second eigenvalue are plotted. Neutral curves are presented for the flow of the fluids with constant viscosity and fluids with a linear dependence of viscosity. The critical flow parameters are shown as functions of the thermoviscosity parameter.
The obtained results show that with increasing thermoviscosity parameter, the critical Reynolds number decreases, and the region of unstable regimes expands. In this case, the critical wave number increases and always exceeds that for the isothermal fluid flow. At very small thermoviscosity parameters, the critical wave and Reynolds numbers for the thermoviscous fluid flow and isothermal fluid flow coincide.
Thus, when determining the conditions for the laminar-to-turbulent transition of the flow regime, it is necessary to take into account the dependence of the viscosity on temperature. The shape of this dependence does not have a significant effect on the critical Reynolds numbers. In this case, the important factor is the non-uniform temperature distribution over the channel cross-section and the corresponding distribution of the fluid viscosity.