On the stability of forced flows with temperature dependent viscosities

This thesis considers the convective stability behaviour of two boundary layer flows:the rotating disk and the at plate. For both coordinate systems, the wall is isothermally heated and fluids with an inverse-linear temperature dependent viscosity are examined. An enforced axial flow is applied to the rotating disk, whilst a variable angle of incline is studied for the plate through solutions to the Falkner-Skan family of equations. For both coordinate systems, similarity solutions are obtained for the mean, laminar flow. It is found that temperature dependencies that reduce the wall viscosity result in a narrowing of the boundary layer for both the disk and the plate, whilst increasing the axial flow strength and angle of incline achieves a similar narrowing of the disk and plate boundary layers, respectively. Linearised stability equations are derived through small perturbations to these mean flows. The stability equations are solved by utilising a spectral method to obtain the disturbance eigen functions and plot curves of neutral stability. With the exception of a small range of flows, temperature dependent viscosity flows are found to be less stable than the temperature independent case in both coordinate systems, where temperature dependence values that produce high wall viscosities yield the least stable flows. Conversely, increasing axial flow strength and angle of incline both produce greater flow stability for their respective geometries. The transitional Reynolds number for these flows is then approximated through an eN type analysis, where it is found to vary in approximate concordance with the critical Reynolds number. Finally, the disturbance eigen functions are used to solve an energy balance integral. Examination of the component energy contributions shows that flow stability is affected exclusively through changes to the mean flow. Extension of this analysis for applications to Chemical Vapour Deposition (CVD) is also discussed.