This article surveys the mathematical principles essential for understanding the thermal management of Li-ion batteries, the current technological state of the art, and the solution. Since the thermal management of electric drive vehicles has environmental, economic, and safety impacts, this review focuses on the efficient methods of battery thermal management (BTM) that were proposed to overcome the major challenges in the electric vehicle industry. The first section examines the perspective of battery-driven vehicles, the principles of Li-ion batteries with a thermal runaway, and their implication for battery safety. The second section discusses mathematical approaches for effective BTM modeling, including the thermal-fluidic network model, lumped capacitance model, spatial resolution lumped capacitance model, equivalent circuit model, impedance-based model, and data-driven model. The third section presents the current state-of-the-art technologies, including air-based, liquid-based, PCM-based, in situ BTM methods, and heat pipe and thermoelectric module-based methods. The conclusion section summarizes the findings from existing research and the possible future directions to achieve and employ better thermal management techniques.

Objects inside cylindrical tubes appear distorted as seen outside the tube due to the refraction of the light passing through different media. Such an optical distortion may cause significant errors in geometrical measurements using optical observations of objects (e.g., liquid-gas interfaces, solid particles, gas bubbles) inside the tubes. In this study, an analytical method using a point-by-point correction of the optical distortion was developed. For an experimental validation, the method was used to correct the apparent profiles of the water-air interfaces (menisci) in cylindrical glass tubes with different tube diameters and wall thicknesses. Then, the corrected meniscus profiles were used to calculate the corrected static contact angles. The corrected contact angle shows an excellent agreement with the reference contact angles as compared to the conventional contact angle measurement using apparent meniscus profiles.