Free surface dynamics of differential type fluids

Abstract

The heart of the thesis discusses thin non-Newtonian fluids. Thin non-Newtonian newline newlineliquid film flows are applicable in many fields. They are used in mucus flow, mi- newlinecrochip production, the flow of surface active material to name a few. This thesis newline newlinestudies the free surface dynamics of fluids of the differential type which is a class newlineof non-Newtonian fluid. This work limits itself to subclasses of fluids known as newline newlinesecond-grade and third-grade fluids. The modeling of such classes of fluids is com- newlineplicated due to the complexity of the constitutive equations. However, the small newline newlineaspect ratio average height of the flow divided by the characteristics length of the newlinedomain simplifies the full model equation. This enables us to use long wave theory newlineto derive the free surface dynamic. Further this thesis intensively discusses the effect newlineof the non-Newtonian parameters and flow surface conditions on thin film thinning newlineand thickening process. A finite volume method using implicit flux discretization newlineis implemented to investigate the viscoelastic effect on the free surface dynamics newlinenumerically. The numerical solution is validated against the available literature newlineresults for the Newtonian case under similar physical conditions. It is observed that newlinethe fluid film over the steady and unsteady stretching surface thins faster with the newlinerapid stretching rate of the sheet, but the second-grade parameter delays the thinning newlinenature of the liquid film. This phenomenon is also observed in a non-isothermal newlinemagneto-hydrodynamic (MHD) fluid flow over steady stretching velocity under newlinethe effect of Lorentz force. The impact of non-invariant fluid parameters such as newlineviscosity, density and thermal conductivity as a linear function of temperature are newlinestudied for an non-isothermal flow of second-grade fluid over a stretching surface. newline