{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T20:33:43Z","timestamp":1767990823445,"version":"3.49.0"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,29]],"date-time":"2022-10-29T00:00:00Z","timestamp":1667001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Based on many previous experiments, the most efficient explicit and stable numerical method to solve heat conduction problems is the leapfrog-hopscotch scheme. In our last paper, we made a successful attempt to solve the nonlinear heat conduction\u2013convection\u2013radiation equation. Now, we implement the convection and radiation terms in several ways to find the optimal implementation. The algorithm versions are tested by comparing their results to 1D numerical and analytical solutions. Then, we perform numerical tests to compare their performance when simulating heat transfer of the two-dimensional surface and cross section of a realistic wall. The latter case contains an insulator layer and a thermal bridge. The stability and convergence properties of the optimal version are analytically proved as well.<\/jats:p>","DOI":"10.3390\/a15110400","type":"journal-article","created":{"date-parts":[[2022,10,29]],"date-time":"2022-10-29T23:45:00Z","timestamp":1667087100000},"page":"400","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Testing Some Different Implementations of Heat Convection and Radiation in the Leapfrog-Hopscotch Algorithm"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7140-3868","authenticated-orcid":false,"given":"Ali Habeeb","family":"Askar","sequence":"first","affiliation":[{"name":"Institute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary"},{"name":"Department of Fluid and Heat Engineering, University of Miskolc, 3515 Miskolc, Hungary"},{"name":"Mechanical Engineering Department, University of Technology\u2014Iraq, Baghdad 10066, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1108-0099","authenticated-orcid":false,"given":"Issa","family":"Omle","sequence":"additional","affiliation":[{"name":"Institute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary"},{"name":"Department of Fluid and Heat Engineering, University of Miskolc, 3515 Miskolc, Hungary"},{"name":"Mechanical Power Engineering Department, Al-Baath University, Homs 77, Syria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0439-3070","authenticated-orcid":false,"given":"Endre","family":"Kov\u00e1cs","sequence":"additional","affiliation":[{"name":"Institute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary"}]},{"given":"J\u00e1nos","family":"Maj\u00e1r","sequence":"additional","affiliation":[{"name":"Institute of Physics and Electrical Engineering, University of Miskolc, 3515 Miskolc, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.12988\/ces.2017.79124","article-title":"Experimental and theoretical study on free and force convection heat transfer","volume":"10","author":"Ochoa","year":"2017","journal-title":"Contemp. 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