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Both solutions are developed from the differential equation that treats these phenomena in Cartesian coordinates, which are modified by geometric correlations and suitable changes of variables to achieve closed\u2010form solutions. The modified differential equations are solved by using two well\u2010known closed\u2010form solutions based on the error function, and then equations are obtained to analyze the diffusion interface position as a function of time and position in cylinders and spheres. These exact correlations are inserted into the closed\u2010form solutions for the slab and are used to update the roots for each radial position of the moving boundary interface. The predictions provided by the proposed analytical solutions are validated against the results of a numerical approach. Finally, a comparative study of diffusion in slabs, cylinders, and spheres is also presented for single\u2010phase and two\u2010phase solid\u2010state diffusion and solidification, which shows the importance of the effects imposed by the radial cylindrical and spherical curvatures with respect to the Cartesian coordinate system in the process kinetics. The analytical model is proved to be general, as far as, a semi\u2010infinite solution for diffusion problems with phase change exists in the form of the error function, which enables exact closed\u2010form analytical solutions to be derived, by updating the root at each radial position the moving boundary interface.<\/jats:p>","DOI":"10.1155\/2021\/6624287","type":"journal-article","created":{"date-parts":[[2021,2,9]],"date-time":"2021-02-09T21:46:48Z","timestamp":1612907208000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On the Transient Atomic\/Heat Diffusion in Cylinders and Spheres with Phase Change: A Method to Derive Closed\u2010Form Solutions"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3118-7125","authenticated-orcid":false,"given":"I. 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