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- All Subjects: Mechanical Engineering
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Description
The heat transfer enhancements available from expanding the cross-section of a boiling microchannel are explored analytically and experimentally. Evaluation of the literature on critical heat flux in flow boiling and associated pressure drop behavior is presented with predictive critical heat flux (CHF) and pressure drop correlations. An optimum channel configuration allowing maximum CHF while reducing pressure drop is sought. A perturbation of the channel diameter is employed to examine CHF and pressure drop relationships from the literature with the aim of identifying those adequately general and suitable for use in a scenario with an expanding channel. Several CHF criteria are identified which predict an optimizable channel expansion, though many do not. Pressure drop relationships admit improvement with expansion, and no optimum presents itself. The relevant physical phenomena surrounding flow boiling pressure drop are considered, and a balance of dimensionless numbers is presented that may be of qualitative use. The design, fabrication, inspection, and experimental evaluation of four copper microchannel arrays of different channel expansion rates with R-134a refrigerant is presented. Optimum rates of expansion which maximize the critical heat flux are considered at multiple flow rates, and experimental results are presented demonstrating optima. The effect of expansion on the boiling number is considered, and experiments demonstrate that expansion produces a notable increase in the boiling number in the region explored, though no optima are observed. Significant decrease in the pressure drop across the evaporator is observed with the expanding channels, and no optima appear. Discussion of the significance of this finding is presented, along with possible avenues for future work.
ContributorsMiner, Mark (Author) / Phelan, Patrick E (Thesis advisor) / Baer, Steven (Committee member) / Chamberlin, Ralph (Committee member) / Chen, Kangping (Committee member) / Herrmann, Marcus (Committee member) / Arizona State University (Publisher)
Created2013
Description
Rabies is an infectious viral disease. It is usually fatal if a victim reaches the rabid stage, which starts after the appearance of disease symptoms. The disease virus attacks the central nervous system, and then it migrates from peripheral nerves to the spinal cord and brain. At the time when the rabies virus reaches the brain, the incubation period is over and the symptoms of clinical disease appear on the victim. From the brain, the virus travels via nerves to the salivary glands and saliva.
A mathematical model is developed for the spread of rabies in a spatially distributed fox population to model the spread of the rabies epizootic through middle Europe that occurred in the second half of the 20th century. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. Since the model assumes these two kinds of rabid foxes, it is a system of both partial differential and integral equations (with integration
over space and, occasionally, also over time). To study the spreading speeds of the rabies epidemic, the model is reduced to a scalar Volterra-Hammerstein integral equation, and space-time Laplace transform of the integral equation is used to derive implicit formulas for the spreading speed. The spreading speeds are discussed and implicit formulas are given for latent periods of fixed length, exponentially distributed length, Gamma distributed length, and log-normally distributed length. A number of analytic and numerical results are shown pertaining to the spreading speeds.
Further, a numerical algorithm is described for the simulation
of the spread of rabies in a spatially distributed fox population on a bounded domain with Dirichlet boundary conditions. I propose the following methods for the numerical approximation of solutions. The partial differential and integral equations are discretized in the space variable by central differences of second order and by
the composite trapezoidal rule. Next, the ordinary or delay differential equations that are obtained this way are discretized in time by explicit
continuous Runge-Kutta methods of fourth order for ordinary and delay differential systems. My particular interest
is in how the partition of rabid foxes into
territorial and diffusing rabid foxes influences
the spreading speed, a question that can be answered by purely analytic means only for small basic reproduction numbers. I will restrict the numerical analysis
to latent periods of fixed length and to exponentially
distributed latent periods.
The results of the numerical calculations
are compared for latent periods
of fixed and exponentially distributed length
and for various proportions of territorial
and wandering rabid foxes.
The speeds of spread observed in the
simulations are compared
to spreading speeds obtained by numerically solving the analytic formulas
and to observed speeds of epizootic frontlines
in the European rabies outbreak 1940 to 1980.
A mathematical model is developed for the spread of rabies in a spatially distributed fox population to model the spread of the rabies epizootic through middle Europe that occurred in the second half of the 20th century. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. Since the model assumes these two kinds of rabid foxes, it is a system of both partial differential and integral equations (with integration
over space and, occasionally, also over time). To study the spreading speeds of the rabies epidemic, the model is reduced to a scalar Volterra-Hammerstein integral equation, and space-time Laplace transform of the integral equation is used to derive implicit formulas for the spreading speed. The spreading speeds are discussed and implicit formulas are given for latent periods of fixed length, exponentially distributed length, Gamma distributed length, and log-normally distributed length. A number of analytic and numerical results are shown pertaining to the spreading speeds.
Further, a numerical algorithm is described for the simulation
of the spread of rabies in a spatially distributed fox population on a bounded domain with Dirichlet boundary conditions. I propose the following methods for the numerical approximation of solutions. The partial differential and integral equations are discretized in the space variable by central differences of second order and by
the composite trapezoidal rule. Next, the ordinary or delay differential equations that are obtained this way are discretized in time by explicit
continuous Runge-Kutta methods of fourth order for ordinary and delay differential systems. My particular interest
is in how the partition of rabid foxes into
territorial and diffusing rabid foxes influences
the spreading speed, a question that can be answered by purely analytic means only for small basic reproduction numbers. I will restrict the numerical analysis
to latent periods of fixed length and to exponentially
distributed latent periods.
The results of the numerical calculations
are compared for latent periods
of fixed and exponentially distributed length
and for various proportions of territorial
and wandering rabid foxes.
The speeds of spread observed in the
simulations are compared
to spreading speeds obtained by numerically solving the analytic formulas
and to observed speeds of epizootic frontlines
in the European rabies outbreak 1940 to 1980.
ContributorsAlanazi, Khalaf Matar (Author) / Thieme, Horst R. (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Baer, Steven (Committee member) / Gardner, Carl (Committee member) / Kuang, Yang (Committee member) / Smith, Hal (Committee member) / Arizona State University (Publisher)
Created2018
Description
There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.
ContributorsPeace, Angela (Author) / Kuang, Yang (Thesis advisor) / Elser, James J (Committee member) / Baer, Steven (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
Realistic engineering, physical and biological systems are very complex in nature, and their response and performance are governed by multitude of interacting processes. In computational modeling of these systems, the interactive response is most often ignored, and simplifications are made to model one or a few relevant phenomena as opposed to a complete set of interacting processes due to a complexity of integrative analysis. In this thesis, I will develop new high-order computational approaches that reduce the amount of simplifications and model the full response of a complex system by accounting for the interaction between different physical processes as required for an accurate description of the global system behavior. Specifically, I will develop multi-physics coupling techniques based on spectral-element methods for the simulations of such systems. I focus on three specific applications: fluid-structure interaction, conjugate heat transfer, and modeling of acoustic wave propagation in non-uniform media. Fluid-structure interaction illustrates a complex system between a fluid and a solid, where a movable and deformable structure is surrounded by fluid flow, and its deformation caused by fluid affects the fluid flow interactively. To simulate this system, two coupling schemes are developed: 1) iterative implicit coupling, and 2) explicit coupling based on Robin-Neumann boundary conditions. A comprehensive verification strategy of the developed methodology is presented, including a comparison with benchmark flow solutions, h-, p- and temporal refinement studies. Simulation of a turbulent flow in a channel interacting with a compliant wall is attempted as well. Another problem I consider is when a solid is stationary, but a heat transfer occurs on the fluid-solid interface. To model this problem, a conjugate heat transfer framework is introduced. Validation of the framework, as well as studies of an interior thermal environment in a building regulated by an HVAC system with an on/off control model with precooling and multi-zone precooling strategies are presented. The final part of this thesis is devoted to modeling an interaction of acoustic waves with the fluid flow. The development of a spectral-element methodology for solution of Lighthill’s equation, and its application to a problem of leak detection in water pipes is presented.
ContributorsXu, Yiqin (Author) / Peet, Yulia (Thesis advisor) / Huang, Huei-Ping (Committee member) / Herrmann, Marcus (Committee member) / Adrian, Ronald (Committee member) / Baer, Steven (Committee member) / Arizona State University (Publisher)
Created2021