Influence of Temperature Dependence of Viscosity on the Stability of Fluid Flow in an Annular Channel

In the present work a detailed numerical study on the eigenvalue spectra for the stability equations of thermoviscous fluid flow in an non-isothermal annular channel was performed. The temperature dependence of viscosity had the form of exponential function that decreases with increasing temperature and was described with the single numerical value called ‘‘thermoviscous parameter’’. The perturbation of the temperature was taken into account and, as a result, the spectral problem was reduced to the system of two coupled ordinary differential equations for axial velocity and temperature perturbations. Eigenvalue spectra for different values of the thermoviscous parameter and the radii of outer and inner cylinders ratio were obtained. The real and imaginary parts of eigenfunctions for eigenvalues from different parts of the spectra were plotted. It was found that for narrow annular channels and rather small values of the thermoviscous parameter the eigenvalue spectra are identical to the ones for isothermal flow in a flat channel. As the thermoviscous parameter increases and the annular channel gap expands the structure of the spectra changes (namely, the spread of eigenvalues along the real axis increases) which leads to the flow stabilization. The eigenfunctions demonstare a non-trivial oscillating distribution of amplitude over the channel cross sections. It can also be mention that the eigenfunctions are not symmetrical, since the undisturbed velocity profile in annular channel also does not have symmetry.