A Numerical Study of Vorticity-enhanced Heat Transfer

To my parents iii ACKNOWLEDGEMENTS I would like to thank my advisor, Dr. for many stimulating conversations, for sharing their enthusiasm for mathematics, and for the invaluable guidance and patience in completing this research. It's a pleasure to thank Dr. Howie Weiss for involving me in the research of microbial population dynamics and providing me the opportunity to explore wider research topics. I'm grateful to Dr. Yingjie Liu for many inspiring discussions on numerical schemes and methods. I would also like to thank the other members of my committee, Dr. Edmond Chow and Dr. Jack Poulson for sharing their insights in scientific computing and providing valuable ideas on my research. I am truly indebted to the grad-coordinators of school of mathematics, Dr. Luca Dieci and Dr. John Etnyre for their help and guidance in many academic and non-academic issues. I thank Yunlong He and Jingfang Liu for many inspiring discussions and perspectives on scientific computing, and I also thank Qingqing Liu and Rundong Du for stimulating office conversations and great help in many aspects. My friends have always been a source of entertainment, exploration, and stress release. Those of note for their great accompanies as roommates. Finally, I'm deeply grateful to my father and mother for all the support that they have given me through the years. You have kept me who I am.