Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform method

Abstract

Lithium-ion batteries (LIBs) have powered the modern world to propel electric vehicles (EVs) and renewable energy sources. These technologies demand higher efficiency and reliability, thereby providing robust mathematical methods are essential for optimizing species diffusion in lithium-ion (Li-ion) cells. However, there is a notable scarcity of literature addressing time-dependent flux boundary conditions with closed-form solutions. In this work, the solid-phase diffusion problem for thin-film and spherical electrodes is considered and tackled using the novel methods Laplace transform-based differential transform method (LT-DTM) and Laplace transform-based $\alpha$-parametrized differential transform method (LT-$\alpha$PDTM). The problem considered is based on Fick's second law and is represented as a partial differential equation (PDE). The modelled PDE is converted to its dimensionless form using suitable dimensionless variables. The resultant non-dimensional PDE is solved using LT-DTM and LT-$\alpha$PDTM. The efficiency of the proposed methods are validated by comparison with previous studies. The results reveal that the proposed methods can analyze presented solid-phase diffusion problems by reducing computational domain size and require fewer iterations to obtain closed-form solutions. Furthermore, this work enhances the theoretical understanding of diffusion in Li-ion cells, improving their effectiveness and performance by offering powerful tools for optimizing electrochemical energy conversion and storage devices.