{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T15:21:36Z","timestamp":1767194496152,"version":"3.48.0"},"reference-count":62,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T00:00:00Z","timestamp":1766966400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Graduate Studies and Scientific Research at Qassim University","award":["QU-APC-2025"],"award-info":[{"award-number":["QU-APC-2025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This article investigates the influence of wall permeability on channel flows and addresses the lack of studies that quantify entropy generation in magnetized Casson fluid models using wavelet-based numerical schemes. We introduce a Fibonacci Wavelet Collocation Method (FWCM) to efficiently solve the transformed nonlinear ordinary differential equations and demonstrate its applicability to the coupled momentum and energy equations. The analysis includes detailed graphical and numerical evaluations of entropy generation, temperature, and velocity fields, along with the Bejan number, Nusselt number, and skin-friction variations. The results reveal that entropy generation increases by approximately 18\u201322% with a higher Biot number and by nearly 15% with increasing Grashof number, while it decreases by about 12% for higher Eckert numbers. Magnetic field strength exhibits a dual effect, producing both suppressing and enhancing behaviors depending on parameter ranges. The FWCM solutions show strong agreement with previously published data, confirming both accuracy and robustness.<\/jats:p>","DOI":"10.3390\/axioms15010029","type":"journal-article","created":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T15:05:01Z","timestamp":1767193501000},"page":"29","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Entropy and Heat Transfer in Casson-MHD Flow Through Inclined Permeable Channels via Fibonacci Wavelets"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5103-6092","authenticated-orcid":false,"given":"Azhar","family":"Iqbal","sequence":"first","affiliation":[{"name":"Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Vivek","sequence":"additional","affiliation":[{"name":"Applied Sciences and Humanities Department, KIET Deemed to be University, Delhi NCR, Ghaziabad 201206, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8309-6121","authenticated-orcid":false,"given":"Khidir Shaib","family":"Mohamed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alawia","family":"Adam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4681-9885","authenticated-orcid":false,"given":"Waseem Ahmad","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2554-1201","authenticated-orcid":false,"given":"Wei Sin","family":"Koh","sequence":"additional","affiliation":[{"name":"Faculty of Business and Communications, INTI International University, Nilai 71800, Negeri Sembilan, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1465","DOI":"10.1063\/1.1694915","article-title":"Laminar flow in a rectangular duct bounded by a porous wall","volume":"17","author":"Sparrow","year":"1974","journal-title":"Phys. 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