{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T10:49:58Z","timestamp":1770979798014,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,22]],"date-time":"2019-12-22T00:00:00Z","timestamp":1576972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The National Science Foundation of China","award":["11771389 and 11621101"],"award-info":[{"award-number":["11771389 and 11621101"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The current article aims to present a numerical analysis of MHD Williamson nanofluid flow maintained to flow through porous medium bounded by a non-linearly stretching flat surface. The second law of thermodynamics was applied to analyze the fluid flow, heat and mass transport as well as the aspects of entropy generation using Buongiorno model. Thermophoresis and Brownian diffusion is considered which appears due to the concentration and random motion of nanoparticles in base fluid, respectively. Uniform magnetic effect is induced but the assumption of tiny magnetic Reynolds number results in zero magnetic induction. The governing equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations. The numerical method is used for solving the so-formulated highly nonlinear problem. The graphical presentation of results highlights that the heat flux receives enhancement for augmented Brownian diffusion. The Bejan number is found to be increasing with a larger Weissenberg number. The tabulated results for skin-friction, Nusselt number and Sherwood number are given. A decent agreement is noted in the results when compared with previously published literature on Williamson nanofluids.<\/jats:p>","DOI":"10.3390\/e22010018","type":"journal-article","created":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T03:15:01Z","timestamp":1577070901000},"page":"18","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":205,"title":["Entropy Generation and Consequences of Binary Chemical Reaction on MHD Darcy\u2013Forchheimer Williamson Nanofluid Flow Over Non-Linearly Stretching Surface"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5880-9553","authenticated-orcid":false,"given":"Ghulam","family":"Rasool","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Yuquan Campus, Hangzhou 310027, China"},{"name":"College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China"}]},{"given":"Ting","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Yuquan Campus, Hangzhou 310027, China"}]},{"given":"Ali J.","family":"Chamkha","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7186-7216","authenticated-orcid":false,"given":"Anum","family":"Shafiq","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China"}]},{"given":"Iskander","family":"Tlili","sequence":"additional","affiliation":[{"name":"Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"},{"name":"Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam"}]},{"given":"Gullnaz","family":"Shahzadi","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, \u00c9cole de Technologie Sup\u00e9rieure, \u00c9TS, Montreal, QC H3C 1K3, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,22]]},"reference":[{"key":"ref_1","unstructured":"Choi, S.U.S., and Eastman, J.A. 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