{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T12:01:59Z","timestamp":1769169719634,"version":"3.49.0"},"reference-count":37,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,9]],"date-time":"2021-11-09T00:00:00Z","timestamp":1636416000000},"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>In the current work, we have investigated the flow past a semi-infinite porous solid media, after presenting a similarity transformation, governing equations mapped to a system of non-linear PDE. The flow of a dusty fluid and heat transfer through a porous medium have few applications, viz., the polymer processing unit of a geophysical, allied area, and chemical engineering plant. Further, we had the option to get an exact analytical solution for the velocity to the equation that is non-linear. The highlight of the current work is the flow of hybrid dusty nanofluid due to Darcy porous media through linear thermal radiation with the assistance of an analytical process. The hybrid dusty nanofluid has significant features improving the heat transfer process and is extensively developed in manufacturing industrial uses. It was found that the basic similarity equations admit two phases for both stretching\/shrinking surfaces. The existence of computation on velocity and temperature profile is presented graphically for different estimations of various physical parameters.<\/jats:p>","DOI":"10.3390\/computation9110118","type":"journal-article","created":{"date-parts":[[2021,11,9]],"date-time":"2021-11-09T12:46:23Z","timestamp":1636461983000},"page":"118","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":29,"title":["Darcy Brinkman Equations for Hybrid Dusty Nanofluid Flow with Heat Transfer and Mass Transpiration"],"prefix":"10.3390","volume":"9","author":[{"given":"K. N.","family":"Sneha","sequence":"first","affiliation":[{"name":"Department of Mathematics, Davangere University, Shivagangothri, Davangere 577 007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"U. S.","family":"Mahabaleshwar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Davangere University, Shivagangothri, Davangere 577 007, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8876-9361","authenticated-orcid":false,"given":"Rachid","family":"Bennacer","sequence":"additional","affiliation":[{"name":"CNRS (Centre National de la Recherche Scientifique), LMT (Laboratoire de M\u00e9canique et Technologie\u2014Labo. M\u00e9ca. Tech.), Universit\u00e9 Paris-Saclay, ENS (Ecole National Sup\u00e9rieure) Paris-Saclay, 91190 Gif-sur-Yvette, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammed EL.","family":"Ganaoui","sequence":"additional","affiliation":[{"name":"Institut Universitaire de Technologie de Longwy, Universit\u00e9 de Lorraine 186 rue de Lorraine, 54400 Cosnes et Romain, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1002\/aic.690070108","article-title":"Boundary-Layer behavior on continuous solid surface, Boundary Layer equation for Two-Dimensional and Axisymmetric Flow","volume":"7","author":"Sakiadis","year":"1961","journal-title":"AIChE J."},{"key":"ref_2","first-page":"645","article-title":"Flow past a stretching plate","volume":"21","author":"Crane","year":"1970","journal-title":"Z. Angew Math. 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