| Fluid flow and heat transfer problems involving interfaces typically contain property jumps and length and time scale disparities, resulting in computational stiffness, demanding resolution requirements due to nonlinearity and multiple physical mechanisms. In this dissertation, both continuum and kinetic approaches are investigated to address the multi-scale thermo-fluid problems, especially those involving interfaces. A continuum model based on the Navier-Stokes fluid model and the Fourier law for heat transfer was employed to investigate the conjugate heat transfer problem. The problem is motivated by recent advancement in the micro-electro-mechanical systems (MEMS) devices for shear stress measurement. Due to the length scale disparity and large solid-fluid thermal conductivity ratio, a two-level computation is used to examine the relevant physical mechanisms and their influences on wall shear stress. The substantial variations in transport properties between the fluid and solid phases and their interplay in regard to heat transfer and near-wall fluid flow structures are investigated. It is demonstrated that for the state-of-the-art sensor design, the buoyancy effect can noticeably affect the accuracy of the shear stress measurement.; A lattice Boltzmann equation (LBE) model derived from the kinetic consideration is investigated to address (i) error behavior due to variable viscosity, and (ii) the interfacial fluid dynamics of some two-phase flow problems. It is shown that the boundary treatment error does not have a significant interaction with the truncation error associated with variable viscosity, and the LBE model closely matches the Navier-Stokes model for fluid flows with large viscosity variation.; Next, an improved interface lattice Boltzmann model is developed for two-phase interfacial fluid dynamics with large property variations. In order to suppress numerical instabilities associated with the presence of the interface, the following approaches were investigated: (i) a new surface tension formulation originated from the diffusion interface method was used to remove unphysical pressure wiggles across interfaces; (ii) a filter scheme was used in numerical gradient calculations to maintain monotonic property variations; (iii) a volume-correction procedure was devised. The performance of the improved LBE model was evaluated using the Rayleigh-Taylor instability problem, stationary bubble under force equilibrium, capillary waves, and rising bubbles. The computational results demonstrated that this LBE two-phase model is more robust than those reported in the literature, capable of treating larger density ratio up to order O(102), while confining the interface thickness within 5-6 grids. |
