{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:34:39Z","timestamp":1760142879540,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T00:00:00Z","timestamp":1704844800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>A two-dimensional heat diffusion problem with a heat source that is a quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are employed. As the problem is nonlinear, Picard\u2019s successive approximation theorem is utilized. We demonstrate the existence, uniqueness, and constant dependence of the solution on the data using the generalized Fourier method under specific conditions of natural regularity and consistency imposed on the input data. For the numerical solution, an implicit finite difference scheme is used. The results obtained from the analytical and numerical solutions closely match each other.<\/jats:p>","DOI":"10.3390\/computation12010011","type":"journal-article","created":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T07:50:48Z","timestamp":1704873048000},"page":"11","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analytical and Numerical Investigation of Two-Dimensional Heat Transfer with Periodic Boundary Conditions"],"prefix":"10.3390","volume":"12","author":[{"given":"\u0130rem","family":"Ba\u011flan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Kocaeli University, TR-41380 Kocaeli, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8595-6092","authenticated-orcid":false,"given":"Erman","family":"Aslan","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Kocaeli University, TR-41380 Kocaeli, T\u00fcrkiye"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/j.ijheatmasstransfer.2012.10.024","article-title":"Mathematical model on surface reaction diffusion in the presence of chemical reaction","volume":"57","author":"Permikin","year":"2013","journal-title":"Int. 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