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.

Two-dimensional (2D) transient numerical thermal modeling was undertaken using ansys fluent v12.1 software to estimate distribution of soil backfill temperatures in a typical mechanically stabilized earth (MSE) wall. The modeling was calibrated using field-measured temperature data from the Tanque-Verde MSE wall in Tucson, Arizona (AZ) in which computed temperature data were found to be within ±5% of the field data. The calibrated model predictions for Las Vegas, Nevada (NV) showed an overall average soil backfill temperature of 34.3 °C relative to a maximum outside surface temperature of 51.6 °C. Such a high average soil backfill temperature calls for modification of design procedures since conventional designs are based on geosynthetic tensile strength determined at 20 °C.

Numerical results of plasma supported deflagration to detonation transition have been presented. The mathematical model includes Reynolds averaged Navier-Stokes equations for the compressible medium, enthalpy equation, the standard k- $\omega$ turbulence model, transport equations for the progress variable and flame wrinkling factor. Non-equilibrium plasma was modeled as a source of radicals. Initial concentrations of radicals were taken from the detailed plasma simulation using a three-temperature plasma model. To model equilibrium plasma we used a Joule heating source with the conductivity depending on the energy deposition time. Simulations showed that the injection of radicals was more efficient than a thermal effect of plasma in the deflagration to detonation transition time and distance. We observed changes in the detonation cell size and improvement of the detonation structure stability with the plasma addition. Because the oxygen atoms injection primarily controls the phenomenon, the detonation cell size depends on the oxygen atoms concentration and on the orientation of the plasma energy spot with respect to the detonation wave.

The effect of a self-pulsing non-equilibrium plasma discharge on piezoelectric PVDF nanofiber membrane was investigated. The plasma discharge was generated in air with a DC power source, with a discharge current of 0.012 mA, a nominal interelectrode separation of 1 mm, and discharge voltage of ~970 V. In a continuous fabrication process, the electrospinning method was used to generate thin nanofiber membrane with a flow rate of 0.7–1 mL h⁻¹ and 25–27 kV voltage to obtain the nanofiber with high sensitivity and a higher degree of alignment and uniformity over a larger area. Plasma treatment was applied on both single layer and multi-layer (three layers) nanomembranes. In addition, simultaneously, the nanofiber membranes were heat-treated at a glass transition temperature (80–120 °C) and then underwent plasma treatment. Fourier-transform infrared (FTIR) spectroscopy showed that the area under the curve at 840 and 1272 cm⁻¹ (β phase) increased due to the application of plasma and differential scanning calorimeter (DSC) indicated an increase in the degree of crystallinity. Finally, PVDF sensors were fabricated from the nanofibers and their piezoelectric properties were characterized. The results suggested that compared to the pristine samples the piezoelectric properties in the plasma and plasma-heat-treated sensors were enhanced by 70% and 85% respectively.

Dynamics of plasma generated by the dual-pulse laser in a supersonic flow was studied numerically. The mathematical model includes species, momentum, electronic, vibrational and translational energy equations for the multicomponent ionized air. The model examines temporal dynamics of the formed air plasma and how it affects the drag, pressure signature and vorticity generation in a supersonic flow around a wedge. We observed that nonequilibrium plasmas is more effective in the drag reduction compared with the simultaneous thermal energy addition. The maximum drag reduction of around 50% and the maximum drag coefficient reduction of 30% was attained through the dual-pulse laser energy deposition. Variation of the plasma spot orientation did not significantly influence the drag reduction. We suggested that the surface pressure changes were not controlled by the vorticity generation but occurred due to the density changes and the formation of the low-density plasma spot.

Combustion involves the study of multiphysics phenomena that includes fluid and chemical kinetics, chemical reactions and complex nonlinear processes across various time and space scales. Accurate simulation of combustion is essential for designing energy conversion systems. Nonetheless, due to its multiscale, multiphysics nature, simulating these systems at full resolution is typically difficult. The massive and complex data generated from experiments and simulations, particularly in turbulent combustion, presents both a challenge and a research opportunity for advancing combustion studies. Machine learning facilitates data-driven techniques to manage the substantial amount of combustion data that is either obtained through experiments or simulations, and thereby can find the hidden patterns underlying these data. Alternatively, machine learning models can be useful to make predictions with comparable accuracy to existing models, while reducing computational costs significantly. In this era of big data, machine learning is rapidly evolving, offering promising opportunities to explore its integration with combustion research. This work provides an in-depth overview of machine learning applications in turbulent combustion modeling and presents the application of machine learning models: Decision Trees (DT) and Random Forests (RF), for the spatio-temporal prediction of plasma-assisted ignition kernels, based on the initial degree of ionization, with model validations against DNS data. The results demonstrate that properly trained machine learning models can accurately predict the spatio-temporal ignition kernel profile based on the initial energy deposition and distribution.