Here I would like to express my most sincere appreciation and gratitude to my supervisor, Professor Chan Siew Hwa, for his considerate guidance and encouragement all throughout this PhD project. I have learnt so much for his expertise in the fields of solid oxide fuel cells and mathematical modelling. More than a supervisor, it is his personality, lifestyle, and working philosophy that inspire me all through this four-year odyssey. I thank Dr. Liu Qinglin for his initial effort on launching this PhD project. I also thank Mr. Chen Xinbing, Mr. Alireza Babaei, and Dr. Zhang Lan for miscellaneous discussions. Mr. Zhao Cunlu is acknowledged for introducing me the computational tool, Wolfram Mathematica ® 7. Ms. Fang Yanan (School of MSE) is acknowledged for her kindly help in X-ray powder diffraction characterization. My warmest acknowledgement goes to Dr. Fu Changjing for insightful discussions over versatile project topics. My thanks also extend to all technicians in Fuel Cell Laboratory (ERI@N), Materials Laboratory A, and Computer Aided Engineering Laboratory for technical guidance and assistance.