preprints_ui: ktcde_v1

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ktcde_v1 An analytical solution to the Navier–Stokes equation for incompressible flow around a solid sphere This paper is concerned with obtaining a formulation for the flow past a sphere in a viscous and incompressible fluid, building upon previously obtained well-known solutions that were limited to small Reynolds numbers. Using a method based on a summation of separation of variables, we develop a general analytical solution to the Navier--Stokes equation for the special case of axially symmetric two-dimensional flow around a sphere. For a particular set of mathematical conditions, the solution can be expressed generally as a hypergeometric function. It reproduces streamlines and flow velocities close to a moving sphere, and provides the angular location immediately behind the sphere where there is a separation between laminar flow and a stagnant region. To produce eddies around a fast-moving sphere, we present a solution obtained using a variable substitution that does not require the separation of variables and is a function of Bessel functions of the first and second kind. For particular boundary conditions, it exhibits eddies behind a fast-moving sphere. 2020-08-22T18:09:49.189512 2021-02-08T21:35:24.270946 2020-08-25T16:24:08.582526     eartharxiv 0 withdrawn 1 1 https://doi.org/10.31223/osf.io/ktcde GNU Lesser General Public License (LGPL) 2.1 Bessel functions of the first kind; Bessel functions of the second kind; Legendre functions of the first kind; Legendre functions of the second kind; Navier–Stokes equation; angle of separation; associated Legendre function of the first kind; hypergeometric function; modified Bessel functions of the first kind; modified Bessel functions of the second kind; partial differential equation; stream function ["Bessel functions of the first kind", "Bessel functions of the second kind", "Legendre functions of the first kind", "Legendre functions of the second kind", "Navier\u2013Stokes equation", "angle of separation", "associated Legendre function of the first kind", "hypergeometric function", "modified Bessel functions of the first kind", "modified Bessel functions of the second kind", "partial differential equation", "stream function"] Ahmad Talaei; Timothy J. Garrett [{"id": "wrq26", "name": "Ahmad Talaei", "index": 0, "orcid": "0000-0003-4603-5666", "bibliographic": true}, {"id": "kcuz8", "name": "Timothy J. Garrett", "index": 1, "orcid": null, "bibliographic": true}] Ahmad Talaei Physical Sciences and Mathematics; Applied Mathematics; Partial Differential Equations; Special Functions; Earth Sciences; Physics; Fluid Dynamics; Engineering; Mechanical Engineering; Other Mechanical Engineering [{"id": "59ea64a954be8111216c1395", "text": "Physical Sciences and Mathematics"}, {"id": "59ea64a954be8111216c13b0", "text": "Applied Mathematics"}, {"id": "59ea64a954be8111216c13b1", "text": "Partial Differential Equations"}, {"id": "59ea64a954be8111216c13b5", "text": "Special Functions"}, {"id": "59ea64aa54be8111216c13d9", "text": "Earth Sciences"}, {"id": "59ea64ab54be8111216c13f8", "text": "Physics"}, {"id": "59ea64ab54be8111216c1401", "text": "Fluid Dynamics"}, {"id": "59ea64b354be8111216c15d9", "text": "Engineering"}, {"id": "59ea64b354be8111216c15da", "text": "Mechanical Engineering"}, {"id": "59ea64b354be8111216c15dd", "text": "Other Mechanical Engineering"}]   0   no not_applicable []   2025-04-09T20:03:48.858774