Hydrodynamics of Incompressible Creeping Couple Stress Fluid Through a Uniformly Porous Channel in Presence of Darcy Resistance: Exact Solution and Physical Insights Using the Inverse Method Approach

Hydrodynamics of Incompressible Creeping Couple Stress Fluid Through a Uniformly Porous Channel in Presence of Darcy Resistance: Exact Solution and Physical Insights Using the Inverse Method Approach | 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 Hydrodynamics of Incompressible Creeping Couple Stress Fluid Through a Uniformly Porous Channel in Presence of Darcy Resistance: Exact Solution and Physical Insights Using the Inverse Method Approach Muhammad Ishaq, Nosheen Fatima, Farkhanda Afzal, Ali Saleh Alshomrani, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3663700/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The current study examines the features of a two-dimensional steady incompressible flow of creeping couple stress fluid across a permeable channel with uniform reabsorption. The mathematical model that governs this flow is composed of linear partial differential equations and homogeneous boundary constraints. The Inverse method approach, an analytical technique, is used to find solutions to the problem. By converting the momentum equations to stream functions, the inverse approach helps derive all the relevant physical quantities, including the longitudinal and transverse velocities, fractional reabsorption, leakage flux, axial pressure, volume flow rate, and mean pressure. Using MATLAB software, the dependent functions such as stream function, pressure, and volume flow are evaluated for different parameter values. The findings indicate that the longitudinal velocity is affected by the initial flow rate, while the transverse velocity shows no change in its profile. The streamlines become more straight and identical as the flow rate increases. Backward flow occurs at the end of the slit due to the porosity parameter. However, the initial flow rate does not impact the transverse velocity of the fluid in the permeable channel. This study fully describes a mathematical foundation for understanding fluid movement across permeable boundaries, which have practical applications in areas such as gaseous diffusion, filtration, and biological mechanisms. Applied Mathematics Plasma and Fluids 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: Posted 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-3663700","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":253059212,"identity":"b595b9be-eec2-4724-873b-23e4edeffcdc","order_by":0,"name":"Muhammad 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