The flow of an inhomogeneous fluid inside a sphere

The research deals with the stationary flow of an inhomogeneous incompressible fluid inside a spherical vessel under the influence of a potential mass force. Using the methods of four-dimensional analysis, the solution to the problem is constructed in an explicit analytical fo...

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Main Authors: Abenov, M.M., Gabbassov, Mars B., Ahmedov, Anvarjon A.
Format: Article
Language:English
Published: Semarak Ilmu Publishing 2022
Subjects:
Online Access:http://umpir.ump.edu.my/id/eprint/44292/
http://umpir.ump.edu.my/id/eprint/44292/1/The%20flow%20of%20an%20inhomogeneous%20fluid%20inside%20a%20sphere.pdf
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author Abenov, M.M.
Gabbassov, Mars B.
Ahmedov, Anvarjon A.
author_facet Abenov, M.M.
Gabbassov, Mars B.
Ahmedov, Anvarjon A.
author_sort Abenov, M.M.
building UMP Institutional Repository
collection Online Access
description The research deals with the stationary flow of an inhomogeneous incompressible fluid inside a spherical vessel under the influence of a potential mass force. Using the methods of four-dimensional analysis, the solution to the problem is constructed in an explicit analytical form.Exact solutions of the Euler equations for a homogeneous fluid are obtained only for some of the simplest problems. Researchers usually prove the existence and uniqueness of solutions to various initial -boundary value problems for Euler equations using the methods of a priori estimation. After that, the problem is usually solved by numerical methods. For an inhomogeneous fluid, when the unknown density is a variable, even obtaining a priori estimates becomes much more complicated, not to mention finding exact solutions. Nevertheless, in recent years, new methods of four-dimensional mathematics have been developed, giving previously unknown approaches to the study of nonlinear problems. In this paper, an exact analytical solution of the Euler equations describing the flow of an ideal inhomogeneous fluid inside a sphere is obtained. At the same time, the authors demonstrate new methods of four-dimensional analysis.
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institution Universiti Malaysia Pahang
institution_category Local University
language English
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publishDate 2022
publisher Semarak Ilmu Publishing
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spelling ump-442922025-04-15T04:18:35Z http://umpir.ump.edu.my/id/eprint/44292/ The flow of an inhomogeneous fluid inside a sphere Abenov, M.M. Gabbassov, Mars B. Ahmedov, Anvarjon A. QA Mathematics TJ Mechanical engineering and machinery The research deals with the stationary flow of an inhomogeneous incompressible fluid inside a spherical vessel under the influence of a potential mass force. Using the methods of four-dimensional analysis, the solution to the problem is constructed in an explicit analytical form.Exact solutions of the Euler equations for a homogeneous fluid are obtained only for some of the simplest problems. Researchers usually prove the existence and uniqueness of solutions to various initial -boundary value problems for Euler equations using the methods of a priori estimation. After that, the problem is usually solved by numerical methods. For an inhomogeneous fluid, when the unknown density is a variable, even obtaining a priori estimates becomes much more complicated, not to mention finding exact solutions. Nevertheless, in recent years, new methods of four-dimensional mathematics have been developed, giving previously unknown approaches to the study of nonlinear problems. In this paper, an exact analytical solution of the Euler equations describing the flow of an ideal inhomogeneous fluid inside a sphere is obtained. At the same time, the authors demonstrate new methods of four-dimensional analysis. Semarak Ilmu Publishing 2022 Article PeerReviewed pdf en cc_by_nc_4 http://umpir.ump.edu.my/id/eprint/44292/1/The%20flow%20of%20an%20inhomogeneous%20fluid%20inside%20a%20sphere.pdf Abenov, M.M. and Gabbassov, Mars B. and Ahmedov, Anvarjon A. (2022) The flow of an inhomogeneous fluid inside a sphere. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 90 (2). pp. 55-63. ISSN 2289-7879. (Published) https://doi.org/10.37934/arfmts.90.2.5563 https://doi.org/10.37934/arfmts.90.2.5563
spellingShingle QA Mathematics
TJ Mechanical engineering and machinery
Abenov, M.M.
Gabbassov, Mars B.
Ahmedov, Anvarjon A.
The flow of an inhomogeneous fluid inside a sphere
title The flow of an inhomogeneous fluid inside a sphere
title_full The flow of an inhomogeneous fluid inside a sphere
title_fullStr The flow of an inhomogeneous fluid inside a sphere
title_full_unstemmed The flow of an inhomogeneous fluid inside a sphere
title_short The flow of an inhomogeneous fluid inside a sphere
title_sort flow of an inhomogeneous fluid inside a sphere
topic QA Mathematics
TJ Mechanical engineering and machinery
url http://umpir.ump.edu.my/id/eprint/44292/
http://umpir.ump.edu.my/id/eprint/44292/
http://umpir.ump.edu.my/id/eprint/44292/
http://umpir.ump.edu.my/id/eprint/44292/1/The%20flow%20of%20an%20inhomogeneous%20fluid%20inside%20a%20sphere.pdf