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In section 1 of this thesis a two-dimensional mathematical model is used to investigate the circulation in a gas-bubble agitation system of a cylindrical vessel for the case of an orifice located at the centre of the base. The two-phase (liquid/gas) region is assumed to be confined to a cone-shaped region and is investigated using Wallis' Drift Flux Model. In the single-phase (liquid) region the turbulent Navier-Stokes equations, written in terms of the stream function, are used for the mathematical model. The analysis in the two-phase region yields the boundary conditions on the two-phase/single-phase boundary. The velocity field in the two-phase region is solved analytically giving results in closed form. A numerical algorithm is developed for calculating liquid flow in the single phase region, and numerical results are presented graphically in terms of the stream function. In section 2 two moving interface problems are investigated. Small time analytic solutions are found for three-dimensional inward solidification of a half space initially at fusion temperature in the first problem. In the second problem, perturbation solutions for melting of a cylindrical annulus with constant heat flux on inner surface are given. In both problems the interface immobilization technique is used. Interface locations at various times are calculated for the inward solidification problem and the results shown in three-dimensional graphs. First and second perturbation terms for the interface location are given for the second problem and graphs of each are presented for a particular case.

This thesis evaluates performance of a non-mechanical conduit valve that was designed for the purpose of this research. The motivation came from the need for a cooling system of portable computers (e.g. laptops and netbooks). As the technology of micro-processors in portable computers advances, they will generate more heat, requiring a more effective and efficient way to cool the system. Based on this fact, a new method of heat dissipation using a single-phase liquid (i.e. water) instead of air was examined. This potentially allowed 80 times more heat dissipation, which translates to better and faster computers for the near future. In designing a single-phase-liquid micro-scale cooling system, various pump mechanisms and their functionalities were considered. It was concluded that a diaphragm pump design is the most effective candidate for this cooling system. The essential component when designing a diaphragm pump is a valve; however, the main issues in selecting a valve are its mechanics and required maintenance. Thus, the non-mechanical valvular conduit, which uses no moving mechanism, was studied through a combination of numerical/computational and experimental methods. The non-mechanical valvular conduit is a micro-channel with a complex geometry; hence, this conduit uses the principle of pressure resistance in the channel flow such that the flow is uni-directional. Through the numerical study, the valvular conduit design’s geometric dimensions were optimized. Then numerical simulations of the pumping/oscillating sequence of the valvular conduit were conducted to examine the effectiveness of the valve when placed in use for a diaphragm pump. It was found that the non-mechanical valve was 38 % more effective in the favorable direction than the opposite direction. As for the necessary heat dissipation, this conduit design demonstrates a great potential to dissipate the thermal design power (TDP) of Intel Pentium D processor (i.e. 130 [W]). During the experiments, the non-mechanical valve confirmed the numerical results. The experimental results also demonstrated that the favorable direction flow produced 244 % less pressure resistance than the opposite direction flow. It was concluded that the non-mechanical valvular conduit can be an effective application for diaphragm pumps in macro and micro-scale without any possibility of obstructing a mechanism.