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Absolute and convective instabilities in the incompressible boundary layer on a rotating disk with temperature-dependent viscosity. (English) Zbl 1189.76222
Summary: The absolute and convective instability of Von-Kármán rotating disk flow with a temperature dependence viscosity of the form \(\mu ^{\prime} = \mu _{\infty }/[1 + \epsilon (T - T_{\infty })/(T_{\omega } - T_{\infty })]\) is investigated. With the use of a spectral method, the linear stability equations are formulated and then solved numerically. Solutions have been obtained for various values of the parameter \(\epsilon \) which controls the temperature dependence of viscosity. It is established the stability of the flow is particularly sensitive to changes in viscosity and even for small positive values of \(\epsilon \) the flow is much more unstable compared to the constant viscosity case.

MSC:
76E15 Absolute and convective instability and stability in hydrodynamic stability
76E07 Rotation in hydrodynamic stability
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76U05 General theory of rotating fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
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