Thermal management continues to be an important topic in engineering research. As the world faces energy shortages, the effective management of thermal energy will be critical to improving energy efficiency. This thesis expands upon advanced thermal management techniques with applications in areas such as electronic cooling, energy conversion, and thermal energy storage using phase change material (PCM). Heat transfer enhancement techniques covered include the development and optimization of novel fin geometries, the effects of natural convection heat transfer with the fin arrangements and during solid-liquid phase change, and magnetohydrodynamic (MHD) enhancement of heat transfer in liquid metals. The thesis is presented in six chapters; an introduction, four technical chapters, and conclusions. Chapters 2-4 feature numerical simulations using COMSOL Multiphysics®. Chapter 2 explores the optimization of Y-shaped fins in a horizontal concentric annular enclosure with natural convection of air. Chapter 3 explores MHD natural convection in the horizontal concentric annular enclosure filled with liquid In-Ga-Sn alloy, with both the Y-shaped and novel “tree-shaped” fins. Chapter 4 uses the In-Ga-Sn alloy in a square enclosure to develop a thermal diode (higher heat transfer in one direction than the opposite) using MHD natural convection. Chapter 5 features both an experimental validation without fins and simulations using the tree-shaped fins to enhance the melting of coconut oil PCM in the horizontal concentric annular enclosure. The conclusions highlight findings and recommendations for future work.