{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T20:40:32Z","timestamp":1782247232956,"version":"3.54.5"},"reference-count":27,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T00:00:00Z","timestamp":1548979200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Chemical reaction in mixed convection magnetohydrodynamic second grade nanoliquid thin film flow through a porous medium containing nanoparticles and gyrotactic microorganisms is considered with entropy generation. The stratification phenomena, heat and mass transfer simultaneously take place within system. Microorganisms are utilized to stabilize the suspended nanoparticles through bioconvection. For the chemical reaction of species, the mass transfer increases. The governing equations of the problem are transformed to nonlinear differential equations through similarity variables, which are solved through a well known scheme called homotopy analysis method. The solution is expressed through graphs and illustrations which show the influences of all the parameters. The residual error graphs elucidate the authentication of the present work.<\/jats:p>","DOI":"10.3390\/e21020139","type":"journal-article","created":{"date-parts":[[2019,2,1]],"date-time":"2019-02-01T11:19:58Z","timestamp":1549019998000},"page":"139","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":58,"title":["Entropy Generation in MHD Mixed Convection Non-Newtonian Second-Grade Nanoliquid Thin Film Flow through a Porous Medium with Chemical Reaction and Stratification"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0991-7846","authenticated-orcid":false,"given":"Noor Saeed","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5539-4225","authenticated-orcid":false,"given":"Zahir","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5263-4871","authenticated-orcid":false,"given":"Saeed","family":"Islam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Khyber Pakhtunkhwa, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2056-9371","authenticated-orcid":false,"given":"Ilyas","family":"Khan","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 736464, Vietnam"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2056-9371","authenticated-orcid":false,"given":"Tawfeeq Abdullah","family":"Alkanhal","sequence":"additional","affiliation":[{"name":"Department of Mechatronics and System Engineering, College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Iskander","family":"Tlili","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Industrial Engineering, College of Engineering, Majmaah University, Al-Majmaah 11952, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Khan, N.S., Zuhra, Z., Shah, Z., Bonyah, E., Khan, W., and Islam, S. 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