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Page IV was not included in the thesis, and thus not included in the page count. / <p> Discretization is an important tool to transfer optimization problems that include differentiations and integrals into standard optimization problems with a finite number of variables and a finite number of constraints. Recently, Betts and Campbell proposed a heat-transfer optimization problem that includes the heat partial differential equation as one of its constraints, and the objective function includes integrals of the temperature function squared. Using discretization methods, this problem can be converted to a convex quadratic optimization problem, which can be solved by standard interior point method solvers in polynomial time.</p> <p> The discretized model of the one dimensional problem is further analyzed, and some of its variants are studied. Extensive numerical testing is performed to demonstrate the power of the "discretize then optimize". Then the heat transfer optimization problem is generalized to two dimensions, and the discretized model and computational comparisons for this variant are included.</p> <p> Flexibility of discretization methods allow us to apply the same "diseretize then optimize" methodology to solve optimization problems that include differential and integral functions as constraints or objectives.</p> / Thesis / Master of Science (MSc)

Effective heat transfer through a bed of particulate solid largely affects the production rate and the process stability in an extrusion process. Most classical models in single screw extrusion treat the solids bed as a continuum behaving as an elastic plug or fluid while neglecting the discrete nature of the particles and the presences of the fluid. The heat transfer within the solids bed in these models is calculated based on thermophysical properties of the bulk system without consideration for the presence of the interstitial fluid. From a practical point of view, experimental measurements of solids bed heat transfer within a rotating screw, particularly cross channel, as the bed moves down the length of the solids conveying zone are impossible to perform. A new device was designed to model the radial compressive stresses and shear stresses on a solids bed of plastics, similar to the environment within the screw channel of a single screw extruder. This device enables the user to visualize the nature of the solids bed under different experimental conditions through a transparent wall. Also, the device provides ways to explore the heat transfer in a solids bed under different conditions by embedded thermocouples on the top or through the front wall of the containing chamber. The results reported in this study have shown that the discrete nature of the solid bed has a strong affect on the heat transfer within the bed. The rate of heat transfer within the different beds of polymer did not appear dominated by the thermophysical properties of the materials. Rather, the evidence supports that conduction through the pseudo-static interstitial fluid (i.e. air) dominated the rate at which a polymer bed heats up; a finding similarly found for the sintering of powdered metals and ceramics in the literature. This finding would imply that differences in melting rates found in extruders are not related to the heat transfer in the solids bed; however, this statement only holds true so long as the granules making up the bed remain static (i.e. plug-like) and do not circulate within the screw channel. Quite interestingly, pellet circulation within the solid bed was observed in LLDPE over a range of test conditions. This pellet circulation resulted in enhanced heat transfer within the bed of LLDPE (a raise of 10°C) compared to PS and PP. PP exhibited pellet circulation but only over a small window of operation. Different ways to improve heat transfer within solid bed were subsequently tested in this project, such as starve feed, forced convection and spherical particle. From this work, improved understanding of heat transfer in the solids conveying zone of a single screw extruder was gained. / Thesis / Master of Applied Science (MASc)

An experimental investigation was performed to study the confined boiling heat transfer characteristics over a saturated porous structure using distilled water as the working fluid. A thin stainless steel resistive foil stretched between two copper electrodes was used to heat a saturated porous plate with an effective pore size of 50 gm. The temperature distribution on the foil heater was measured using a high speed thermal imaging camera. The effect of the gap height between the heater and the porous plate on the heat transfer was investigated for gap heights ranging from 0 um to 1000 um and for heat fluxes ranging from 11.7 kW/m2 to 58.3 kW/m2. It was observed that the highest heat transfer rate was obtained at a gap height of approximately 600 pm. The main heat transfer mechanism is thought to be confined boiling in the small gap between the heating surface and the saturated porous structure. It was observed that the effect of the subcooled liquid temperature did not have a significant effect on the heat transfer. The effect of the pore size in the porous plate was investigated by repeating the measurements with a porous plate of 200 gm pore size. It was observed that the thermal resistance for the plate with a 200 gm pore size was significantly higher than the plate with 50 gm pores for gaps less than 300 gm. At a larger gap height of 600 gm, similar heat transfer performances were obtained for the two porous media. / Thesis / Master of Applied Science (MASc)

Wildfires pose a growing threat for communities along the wildland-urban interface (WUI) around the world driven by a changing climate and expanding urban areas. One of the primary mechanisms by which fires can spread in the WUI are firebrands, airborne embers capable of acting as ignition sources carried in the airstream. Many studies have been conducted on the generation and transport of firebrands, but limited work has been conducted to quantify the heat transfer of firebrand piles to surfaces. A series of three studies are presented here exploring the heat transfer, burning, and material ignition of firebrands. In the first study, the differences between firebrands from structure and vegetation sources was compared. It was found that an ash layer in the vegetation firebrands reduced the heat and mass transfer. In the second study, impact of the surface geometries that firebrands accumulate on was explored. It was found that wall and corner configurations reduced the heat transfer the most and caused piles to burn from the wall surfaces outwards. Flat plate and decking configurations had the highest heat flux due to the lack of flow obstruction. In the final study, a framework was developed for predicting the material ignition resistance reliability exposed to a smoldering firebrand pile. The exposure was based on empirical relations for the heat flux from piles as a function of pile height, porosity, and wind speed. Cone calorimeter data was used to generate material thermal and ignition properties. With these inputs, the framework was used to predict the potential for material ignition thus circumventing the need for costly firebrand tests. This collection of studies provides evidence of the factors that drive firebrand burning behavior and heat transfer and links those aspects to the potential for ignition of construction materials. / Doctor of Philosophy / Wildland-urban interface (WUI) fires pose a growing threat for communities around the world driven by a changing climate and expanding urban areas. A particularly dangerous way that fires can spread long distances is via firebrands, burning particles that splinter off of trees or buildings that can be blown long distances by the wind. These firebrands can land onto surfaces like buildings and ignite those surfaces, causing new fires called spot fires. The science behind how firebrands ignite new surfaces is not well-developed, and there is no broad tool that can be used to predict whether a material or a building will ignite given certain conditions. The research presented here aims to address that lack of understanding by approaching the problem systematically, breaking down the individual driving elements of firebrand burning. First, the difference in heat transfer and burning behavior between firebrands from structures and from vegetation was explored. Second, the impact of various surface geometries was explored. The surface geometry of where the firebrands accumulate also influences the heat transfer of the firebrands. Finally, a framework for predicting the material reliability of materials to firebrand exposure is presented. Experimental correlations for firebrand burning based on pile parameters were generated and used to predict the heat fluxes from piles. The framework used material ignition data from cone calorimeter experiments to predict how materials would respond under thermal exposure. The framework compares the predicted exposure with the material ignition data to calculate the reliability. This collection of studies provides insight on the many factors that drive firebrand burning behavior and heat transfer and links those aspects to the ignition of materials.