Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform method
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)...
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S266681812500035X |
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| author | Shivaranjini S Neetu Srivastava |
| author_facet | Shivaranjini S Neetu Srivastava |
| author_sort | Shivaranjini S |
| collection | DOAJ |
| description | 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 α-parametrized differential transform method (LT-αPDTM). 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-αPDTM. 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. |
| format | Article |
| id | doaj-art-e41c593a459048eab2bd1171dc59720e |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-e41c593a459048eab2bd1171dc59720e2025-02-08T05:01:26ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101107Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform methodShivaranjini S0Neetu Srivastava1Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru, Karnataka, IndiaCorresponding author.; Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru, Karnataka, IndiaLithium-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 α-parametrized differential transform method (LT-αPDTM). 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-αPDTM. 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.http://www.sciencedirect.com/science/article/pii/S266681812500035XBatteriesElectrodesSolid-phase diffusionLaplace transformDifferential transform methodα-Parametrized differential transform method |
| spellingShingle | Shivaranjini S Neetu Srivastava Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform method Partial Differential Equations in Applied Mathematics Batteries Electrodes Solid-phase diffusion Laplace transform Differential transform method α-Parametrized differential transform method |
| title | Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform method |
| title_full | Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform method |
| title_fullStr | Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform method |
| title_full_unstemmed | Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform method |
| title_short | Semi-analytical approach for solving the mathematical model of solid-phase diffusion in electrodes: An application of modified differential transform method |
| title_sort | semi analytical approach for solving the mathematical model of solid phase diffusion in electrodes an application of modified differential transform method |
| topic | Batteries Electrodes Solid-phase diffusion Laplace transform Differential transform method α-Parametrized differential transform method |
| url | http://www.sciencedirect.com/science/article/pii/S266681812500035X |
| work_keys_str_mv | AT shivaranjinis semianalyticalapproachforsolvingthemathematicalmodelofsolidphasediffusioninelectrodesanapplicationofmodifieddifferentialtransformmethod AT neetusrivastava semianalyticalapproachforsolvingthemathematicalmodelofsolidphasediffusioninelectrodesanapplicationofmodifieddifferentialtransformmethod |