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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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