Hydrodynamical Study of Couple Stress Fluid Flow in a Linearly Permeable Rectangular Channel Subject to Darcy Porous Medium and No-Slip Boundary Conditions

Hydrodynamical Study of Couple Stress Fluid Flow in a Linearly Permeable Rectangular Channel Subject to Darcy Porous Medium and No-Slip Boundary Conditions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Hydrodynamical Study of Couple Stress Fluid Flow in a Linearly Permeable Rectangular Channel Subject to Darcy Porous Medium and No-Slip Boundary Conditions Muhammad Ishaq, Saif Ur Rehman, Muhammad Zahid This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3622227/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Feb, 2024 Read the published version in Alexandria Engineering Journal → Version 1 posted You are reading this latest preprint version Abstract In this paper, the study investigates the issue of the creeping flow of a non-Newtonian couple stress fluid through a linearly porous walled slit within a Darcy porous medium. The well-established approach, the Inverse Method approach, was employed to attain the precise solution of the governing equations. The inverse technique is utilized to transform the momentum equations into stream functions. The physical parameters are all computed: longitudinal velocity, transverse velocity, fractional reabsorption, leakage flux, axial pressure, volume flow rate, and mean pressure. The data was also graphed, indicating that the initial flow rate affects longitudinal velocity but not transverse velocity. The initial flow rate significantly impacts streamlines; as the flow rate rises, the streamlines become straighter and more uniform. Physical quantities are also influenced by permeability and the couple stress parameter. Backward flow occurs at the slit’s end due to the porosity parameter. The fluid flow in kidney-diseased renal tubules is the main focus of this study. Some fibrous materials, fatty substances, and solid waste particles, among other things, may become suspended in the tubule channel and in the wall’s pores as a result of illnesses, leading to biofouling and porosity filling in the slit, respectively. Applied Mathematics Couple Stress Fluid Exact solutions Porous Parallel Plates Porous medium Uniform reabsorption Darcy porous medium Creeping flow Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Published Journal Publication published 05 Feb, 2024 Read the published version in Alexandria Engineering Journal → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3622227","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":250139684,"identity":"2d05147d-2f4f-417e-b5f6-425f2cd01234","order_by":0,"name":"Muhammad Ishaq","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBUlEQVRIiWNgGAWjYHACNoYENgkGAwYGxocfKmyAAoyNB4jVwmwscSYNpKWBsBYQAmphk+BtOwwWwqvFvP34swcPyizszdkPb5OQOHPebm37YaAtNTbRuLTInMkxN0g4J5G4syet2KKg4nbytjOJQC3H0nIbcGiRYMhhk0hsk0gwOJBjeEPizO1kswNALYwNh3Fr4X/+DKTF3uD8GwOgX84lm51/SECLRIIZSAvjhhs5RkAtB+zMbhCyReKNmQTILxtuPCsGBnJygtkNoC0J+PzCn/5M8kdZHdBhyRuBUWlnb3Y+/eGDDzU2OLUgAwMQkQhWmUCEcrgWeyIVj4JRMApGwQgCACPlZLoIrYQ+AAAAAElFTkSuQmCC","orcid":"","institution":"COMSATS University Islamabad, Lahore Campus","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Ishaq","suffix":""},{"id":250140104,"identity":"b3087ca0-877c-43bc-9441-ebae7935621b","order_by":1,"name":"Saif Ur Rehman","email":"","orcid":"","institution":"Department of Mathematics, University of Management and Technology Lahore 54770, Pakistan","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Saif","middleName":"Ur","lastName":"Rehman","suffix":""},{"id":250140186,"identity":"7009e430-897e-409f-84f5-420fc4351e5f","order_by":2,"name":"Muhammad Zahid","email":"","orcid":"","institution":"Department of Mechanical Engineering, Lodz University of Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Zahid","suffix":""}],"badges":[],"createdAt":"2023-11-16 20:13:22","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false,"coiExplicitlySet":false},"doi":"10.21203/rs.3.rs-3622227/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3622227/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1016/j.aej.2024.01.066","type":"published","date":"2024-02-06T00:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":51504577,"identity":"0d913321-1ef4-4f5b-9f98-45f1039f791b","added_by":"auto","created_at":"2024-02-22 18:30:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":921210,"visible":true,"origin":"","legend":"","description":"","filename":"33.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3622227/v1_covered_688b8cbd-7b8b-4814-a21f-006715428c92.pdf"}],"financialInterests":"\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e","formattedTitle":"\u003cp\u003eHydrodynamical Study of Couple Stress Fluid Flow in a Linearly Permeable Rectangular Channel Subject to Darcy Porous Medium and No-Slip Boundary Conditions\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":" Lodz University of Technology","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Couple Stress Fluid, Exact solutions, Porous Parallel Plates, Porous medium, Uniform reabsorption, Darcy porous medium, Creeping flow","lastPublishedDoi":"10.21203/rs.3.rs-3622227/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3622227/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, the study investigates the issue of the creeping flow of a non-Newtonian couple stress fluid through a linearly porous walled slit within a Darcy porous medium. 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