| The interaction of heat, mass, and momentum transfer are especially complex in systems where the highly nonlinear phenomena of exothermic chemical reactions and radiative heat transfer are important. Detailed models of these systems allow the role of each mechanism in the interaction to be independently analyzed and understood, leading to better design and optimization of reaction engineering and materials processing systems. My thesis work concentrates on two problems which involve aspects of transport phenomena and nonlinear systems.; The first system studied is the spontaneous combustion of coal stockpiles, which presents challenges in chemical reactor modeling, computational fluid dynamics, and nonlinear analysis of complex systems. We have developed a model which better represents the real system than previous models by including the fluid dynamics in the coal pile and the surrounding air, instead of only in the porous coal region. Significant qualitative differences in ignition behavior between our results and previous works can be directly attributed to simplifying assumptions of the fluid flow in their models.; Our successful formulation and implementation of the governing equations and boundary conditions for the simultaneous computation of flows in fluid and porous domains should help future researchers to accurately model such systems.; The second project is a fundamental study of the effect of internal radiative heat transfer on buoyancy-driven flows in a cylinder heated from below. Radiation can be an important or even the dominant mode of heat transport in high temperature systems, yet it is often ignored or oversimplified in process models because of computational difficulties inherent in its long range and nonlinear nature. Bifurcation analysis of the governing conservation equations shows the effect of the changes on the characteristic flows states, their connectivity, and their stability. Results encompassing the complete range of optical thicknesses from the opaque to transparent limits add to our understanding of this system.; In addition to these two main projects, I have developed a code on the CM5 parallel computer to solve for three-dimensional fluid flows in simple geometries. These flows are crucial to further the understanding the nonlinear interactions in many reacting and processing systems. |
