Laplace Transform and Bessel Functions in Solving an Electrochemical Corrosion Problem
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Electrochemical corrosion protection of metallic structures, particularly, in oil storage tanks, is a problem of great industrial importance. This paper proposes a mathematical model based on partial differential equations, which can be simplified to an ordinary differential equation with variable coefficients, under certain conditions. The latter is solved using Laplace transform, resulting in a solution expressed in terms of modified Bessel functions.
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Hidalgo J, Hidalgo L, Serrano Aguiar CD, García Madroñero DB, Galambos I, Vilasó-Cadre JE, et al. Study of Caesalpinia spinosa extracts as green corrosion inhibitor for mild steel. Langmuir. 2025;41(14):9406–21. Available from: https://doi.org/10.1021/acs.langmuir.5c00224
Hidalgo J, Cotolan N, Lupan A, Brânzanic AMV, Turdean GL. A poly(methyl methacrylate)–ibuprofen composite film as anticorrosive coating of Ti–6Al–4V surface. J Solid State Electrochem. 2024;28:479–94. Available from: https://doi.org/10.1007/s10008-023-05681-w
Hidalgo J, Hidalgo L, Serrano C, Punina D, Rea E, Ilbay M, et al. A study of the inhibition capacity of a novel Ilex guayusa green extract for preventing corrosion in mild steel exposed to different conditions. Analytica. 2025;6(1). Available from: https://doi.org/10.3390/analytica6010001
Jiao Z, Dong Y, Li Q, Zhou Q. Enhancing tribocorrosion resistance of VCoNi alloys in artificial seawater via nitrogen alloying. Corros Sci. 2025;243:112600. Available from: http://dx.doi.org/10.1016/j.corsci.2024.112600
Siddiqui NA, Muzamil M, Jamil T, Hussain G. Smart materials in manufacturing. Smart Mater Manuf. 2025;3:100080. Available from: https://www.keaipublishing.com/en/journals/smart-materials-in-manufacturing/
Campo L, Martinez-Luaces V, Ohanian M. Sistema de protección catódica interna en tanques de crudo. Montevideo (UY): ANCAP-UdelaR; 2017. Technical report.
Ohanian M, Martinez-Luaces V. Corrosion potential profile simulation in a tube under cathodic protection. Int J Corros. 2014;2014:Article ID 102363. Available from: http://dx.doi.org/10.1155/2014/102363
Martinez-Luaces V, Campo L, Ohanian M. Calculus of the distribution of sacrificial anodes for roof oil tanks cathodic corrosion protection. Adv Math Model Appl. 2019;4(3):224–31. Available from: https://jomardpublishing.com/UploadFiles/Files/journals/AMMAV1N1/V4N3/Martinez-Luaces.pdf
Ibl N. Current distribution. In: Yeager E, Bockris JO, Conway BE, Sarangapani S, editors. Comprehensive Treatise of Electrochemistry. Boston (USA): Springer. 1983;6:239–315. Available from: https://link.springer.com/chapter/10.1007/978-1-4615-6690-8_4
Newman J. Engineering design of electrochemical systems. Ind Eng Chem. 1968;60(4):12–27. Available from: https://pubs.acs.org/doi/10.1021/ie50700a005
Zill DG, Cullen MR. Differential equations with boundary-value problems. Belmont (USA): Cengage Learning; 2009. p. 480–1. Available from: http://www.uop.edu.pk/ocontents/DIFFERENTIAL%20EQUATIONS%20with%20Boundary-Value%20Problemsa%20Zill%20Cullen(1).pdf
Frumkin AN. Distribution of the corrosion process along the tube length. J Phys Chem. 1949;23:1477–82.
Spiegel M, Lipschutz S, Liu J. Schaum's outline of mathematical handbook of formulas and tables. 3rd ed. London (UK): McGraw-Hill Education; 2008. Available from: http://mcb111.org/w01/Mathematical_Handbook_of_Formulas_and_Ta.pdf