Mathematical Modeling of Lithium-ion Batteries and Improving Mathematics Learning Experience for Engineering Students

Abstract

Increase in the world’s energy consumption along with the environmental impacts of conventional sources of energy (gas, petroleum, and coal) makes the shift to clean energy sources unavoidable. To address the energy needs of the world, using clean energy sources would not provide the sufficient answer to the world’s energy issues if it is not accompanied by developing energy storage systems that are capable of storing energy efficiently. Lithium-ion batteries are the main energy storage devices that are developed to satisfy the ever-growing energy needs of the modern world. However, there are still important features of Li-ion battery systems (such as the battery microstructural effects) that need to be studied to a broader extent. In this regard, some of the battery microstructural phenomena, such as the formation of solid electrolyte interface, is believed to be the main reason behind battery degradation and drop in performance. Previous studies have focused on the experimental and computational investigation of micro- and macro- structural features of the Li-ion battery; however, further study is needed to focus on incorporating the effects of microscale features of the Li-ion batteries into the total response of the battery system. In the present work, the details of developing a multiscale mathematical model for a Li-ion battery system is explained, and a multiscale model for the battery system is developed by employing variational multiscale modeling method. The developed model is capable of considering the effects of the battery microstructural features (e.g., the random shape of the active material particles) on the total battery performance. In the developed multiscale framework, the microstructural effects are accounted for in the governing equations of the battery macroscale with the help of Green’s function and variational formulation. This part of the present work provides a clear framework for understanding the details and process of developing a multiscale mathematical model for a Li-ion battery system. Learning mathematics is essential in engineering education and practice. With increasing number of students and emergence of online/distance learning programs, it is critical to look for new approaches in teaching mathematics that different in content development and design. Special consideration should be in place in designing an online program for teaching mathematics to ensure students’ success and satisfaction in the engineering curriculum. Previous investigations studied the effects of enrolling in online programs on students’ achievement. However, more implementations of such educational frameworks are needed to recognize their shortcomings and enhance the quality of online learning programs. In addition, the idea of the blended classroom should be put into practice to a further extent to ensure the high-quality development of online instructional content. In this work, an online learning program was provided for engineering students enrolled in an introductory engineering mechanics course. Online interactive instructional modules were developed and implemented in the targeted engineering course to cover prerequisite mathematical concepts of the course. Students with access to the developed online learning modules demonstrated improvement in their learning and recommended employing such modules to teach fundamental concepts in other courses. This part of the work improves the understanding of the development process of the online learning modules and their implementation in lecture-based classrooms.