{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T13:51:41Z","timestamp":1762005101555,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,13]],"date-time":"2019-06-13T00:00:00Z","timestamp":1560384000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study is about the lubrication of a long porous slider in which the fluid is injected into the porous bottom. The similarity transformation reduces the Navier-Stokes equations to couple nonlinear, ordinary differential equations, which are solved by a new algorithm. The proposed technique is based on integral transformation. Apparently, there is great symmetry between proposed method and variation iteration method, Adomian decomposition method but in integral transform method all the boundary conditions are applied, then a recursive scheme is used for the analytical solutions, which is unlike the Variational Iteration Method, Adomian Decomposition Method, and other existing analytical methods. Solutions are obtained for much larger Reynolds numbers, and they are compared with analytical and numerical methods. Effects of Reynolds number on velocity components are presented.<\/jats:p>","DOI":"10.3390\/sym11060791","type":"journal-article","created":{"date-parts":[[2019,6,13]],"date-time":"2019-06-13T11:15:58Z","timestamp":1560424558000},"page":"791","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Integral Transform Method to Solve the Problem of Porous Slider without Velocity Slip"],"prefix":"10.3390","volume":"11","author":[{"given":"Naeem","family":"Faraz","sequence":"first","affiliation":[{"name":"International Cultural Exchange School of Donghua University, Shanghai 200051, China"},{"name":"Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yasir","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 1803, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6896-172X","authenticated-orcid":false,"given":"Dian Chen","family":"Lu","sequence":"additional","affiliation":[{"name":"Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1285-0593","authenticated-orcid":false,"given":"Marjan","family":"Goodarzi","sequence":"additional","affiliation":[{"name":"Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/j.aej.2013.08.005","article-title":"MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet","volume":"52","author":"Nadeem","year":"2013","journal-title":"Alex. 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