Brinkman Equation in Tangent Sphere and Cardioid Coordinate Systems: Stream Function Solution

Brinkman Equation in Tangent Sphere and Cardioid Coordinate Systems: Stream Function Solution | 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 Brinkman Equation in Tangent Sphere and Cardioid Coordinate Systems: Stream Function Solution Deepak Kumar Maurya, Vikas Kumar Sharma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4378201/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 In the present investigation, we have identified the stream function solution of the Brinkman equation in both the cardioid coordinates (λ, σ, ζ) and tangent sphere coordinates (τ, η, ζ). Trigonometric functions, special functions such as modified Bessel functions and Bessel functions, are contained in the analytical expressions of the stream function and velocity components. We also discussed about how permeability depends on the estimated stream function solution for the Brinkman equation in the cardioid and tangent sphere coordinate systems, which can be deduced as a particular scenario that corresponds with the solution which is currently available [7]. MSC (2020): 35G05, 35C05, 76S05 Applied Mathematics Plasma and Fluids Brinkman equation Stokes equation Modified Bessel’s functions Permeability 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. 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