Computational studies of the heat transfer and fluid flow in lubrication and coating problems.

摘要

The current research is focused on the mathematical modeling and computational implementation of the problems arising in materials processing. In particular, emphasis will be on mixing and coating, including transient and free surface flows of Newtonian and non-Newtonian fluids. In addition, the heat conduction in complex domains will be considered.;A hybrid boundary element method (HBEM) is developed to solve planar steady-state heat conduction problems for domains involving thick and thin regions. Many polymer-processed parts are typically thin, and a thin-shell approach can therefore be used. However, the part usually involves a thick region as well, which is typically present around corners. The proposed formulation consists of combining the thin-shell approximation in the thin sub-domain with conventional BEM in the thick sub-domain. The method is validated upon comparison against the fully BEM approach.;The three-dimensional transient free surface flow inside cavities of arbitrary shape is examined using an adaptive (Lagrangian) boundary-element approach. The fluid is assumed to be incompressible and Newtonian, under creeping conditions. A simple algorithm is developed for mesh refinement of the deforming free surface mesh. The method is used to determine the flow field and free surface evolution inside cubic, rectangular and cylindrical containers. Surface tension effects are also explored.;The three-dimensional Stokes flow in a periodic domain is then investigated. The problem corresponds closely to the flow inside internal mixers, where the flow is driven by the movement of a rotating screw and the outer barrel remaining at rest. A hybrid spectral/finite-difference approach is proposed for the general expansion of the flow field and the solution of the expansion coefficients. The method is used to determine the flow field between the screw and barrel. The regions of elongation and shear are closely examined since these are the two mechanisms responsible for mixing performance.;In this thesis, a heavy emphasis is placed on the flow of Newtonian and non-Newtonian thin films, typically as encountered in transient coating processes. Both two-dimensional and axisymmetric flows are considered. The fluid emerges from a channel (or an annular tube) and is driven by a pressure gradient maintained inside the channel (or annulus). The governing equations dictating the flow are thin-film equations of the 'boundary layer type', which are solved by expanding the flow field in terms of orthonormal modes in the depthwise direction, and using the Galerkin projection, combined with a time-stepping implicit scheme, and integration along the flow direction using a sixth order Runge-Kutta method. The generalized-Newtonian, non-Newtonian as well as viscoelastic fluids are examined to investigate the effect of inertia, gravity and the substrate topography subjected to different initial conditions. In addition, the hyperbolic nature of the thin-film equation is further investigated analytically using the method of characteristics. An excellent agreement has been found in the limit of steady-state flow of a Newtonian fluid upon comparison against the similarity solution for liquid spreading.