A comparative study of different viscosity models for unsteady flow over a decelerating rotating disk with variable physical properties

The classical Von-Kármán infinite disk problem is one of the few fluid mechanics problems that demonstrates both theoretical and practical significance. Furthermore, temperature has a strong effect on fluid viscosity in various fluid situations particularly where considerably high operating temperatures are employed. Momentum and thermal boundary layer formations around a decelerating rotating disk in an otherwise calm environment are considered. Main interest here is to account for the temperature dependency in both viscosity and thermal conductivity. New computational results for liquids with two different viscosity models are derived in this study. Whole analysis is conducted by assuming slip effects at the boundary, which yield non-linear Robbin-type boundary conditions for radial and azimuthal velocity components. In addition, disk is allowed to expand radially with linearly varying velocity. A generalized set of transformations is invoked that enabled a self-similarity analysis of flow model accounting for temperature-dependent properties. For the numerical solution, we relied on a reliable routine bvp4c of software MATLAB. A comparative study of different variable viscosity models is also undertaken. It is concluded that neglecting temperature dependence of viscosity or thermal conductivity can lead to inaccurate predictions of the model