{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,3]],"date-time":"2026-02-03T20:28:48Z","timestamp":1770150528474,"version":"3.49.0"},"reference-count":59,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T00:00:00Z","timestamp":1709164800000},"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>The principal objective of the study is to examine the impact of thermal radiation and entropy generation on the magnetohydrodynamic hybrid nano-fluid, Al2O3\/H2O, flow in a Darcy\u2013Forchheimer porous medium with variable heat flux when subjected to an electric field. Investigating the impact of thermal radiation and non-uniform heat flux on the hybrid nano-liquid magnetohydrodynamic flow in a non-Darcy porous environment produces novel and insightful findings. Thus, the goal of the current study is to investigate this. The non-linear governing equation can be viewed as a set of ordinary differential equations by applying the proper transformations. The resultant dimensionless model is numerically solved in Matlab using the bvp4c command. We obtain numerical results for the temperature and velocity distributions, skin friction, and local Nusselt number across a broad range of controlling parameters. We found a significant degree of agreement with other research that has been compared with the literature. The results show that an increase in the Reynolds and Brinckmann numbers corresponds to an increase in entropy production. Furthermore, a high electric field accelerates fluid velocity, whereas the unsteadiness parameter and the presence of a magnetic field slow it down. This study is beneficial to other researchers as well as technical applications in thermal science because it discusses the factors that lead to the working hybrid nano-liquid thermal enhancement.<\/jats:p>","DOI":"10.3390\/computation12030043","type":"journal-article","created":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T05:59:19Z","timestamp":1709186359000},"page":"43","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Entropy Generation and Thermal Radiation Impact on Magneto-Convective Flow of Heat-Generating Hybrid Nano-Liquid in a Non-Darcy Porous Medium with Non-Uniform Heat Flux"],"prefix":"10.3390","volume":"12","author":[{"given":"Nora M.","family":"Albqmi","sequence":"first","affiliation":[{"name":"Mathematical Modelling and Applied Computation Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Mathematics, Taif University, Taif 21944, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9443-7091","authenticated-orcid":false,"given":"Sivasankaran","family":"Sivanandam","sequence":"additional","affiliation":[{"name":"Mathematical Modelling and Applied Computation Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai 602105, India"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/j.csite.2018.05.002","article-title":"Micropolar nanofluid flow and heat transfer between penetrable walls in the presence of thermal radiation and magnetic field","volume":"12","author":"Alizadeh","year":"2018","journal-title":"Case Stud. 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