{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:44:41Z","timestamp":1760237081165,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,2,24]],"date-time":"2020-02-24T00:00:00Z","timestamp":1582502400000},"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>In this work, Finite Element Method (FEM) is applied to obtain the condition at the boundary of the interface between a channel and a porous medium. The boundary conditions that should be applied to the inhomogeneous interface zone between the two homogeneous regions of free fluid and porous medium are derived. The comparison has been performed for porous material characterizations to provide the velocity at the inhomogeneous interface zone with variable permeability between the two homogeneous regions of free fluid and porous medium. Also, the dependence of the slip coefficient on the thickness of the transition zone is established and the values of the thickness are so justified that the numerical results and the numerical results of our proposed technique are found to be in good agreement with experimental results in the literature.<\/jats:p>","DOI":"10.3390\/computation8010014","type":"journal-article","created":{"date-parts":[[2020,2,25]],"date-time":"2020-02-25T04:21:26Z","timestamp":1582604486000},"page":"14","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Range of Applying the Boundary Condition at Fluid\/Porous Interface and Evaluation of Beavers and Joseph\u2019s Slip Coefficient Using Finite Element Method"],"prefix":"10.3390","volume":"8","author":[{"given":"Azza Hassan","family":"Soliman","sequence":"first","affiliation":[{"name":"Jamoum University College, Umm Al-Qura University, Alshohdaa 25371, Jamoum, Makkah, Saudi Arabia"},{"name":"Faculty of Women for Arts, Science and Education, Ain Shams University, Cairo 11757, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2417-3913","authenticated-orcid":false,"given":"Mohamed Abdelsabour","family":"Fahmy","sequence":"additional","affiliation":[{"name":"Jamoum University College, Umm Al-Qura University, Alshohdaa 25371, Jamoum, Makkah, Saudi Arabia"},{"name":"Faculty of Computers and Informatics, Suez Canal University, New Campus, 4.5 Km, Ring Road, El Salam District, Ismailia 41522, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.cma.2014.10.050","article-title":"Effective interface conditions for the forced infiltration of a viscous fluid into a porous medium using homogenization","volume":"292","author":"Carraro","year":"2015","journal-title":"Comput. 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