School of Mathematics and Statistics - Theses

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Transport equations and boundary conditions for oscillatory rarefied gas flows

Liu, Nicholas Zhixian ( 2018)

A wide range of flow phenomena in everyday life can be modelled accurately using classical continuum theory: the Navier-Stokes equations with associated no-slip conditions. However, oscillatory flows generated by nanoscale devices violate the basic assumptions underpinning continuum theory. Study of such flows, under the assumption of small perturbations from equilibrium, requires analysis of the unsteady Boltzmann equation. At sufficiently high oscillation frequencies, the resulting flow can result in wave propagation. This thesis presents a rigorous asymptotic analysis of slightly rarefied wave motion. Particular emphasis is placed on the boundary layer structure, transport equations and associated slip boundary conditions, valid for a general curved oscillating boundary with a velocity-independent body force.