Numerical Solution of Oxygen Diffusion Problem in Spherical Cell
This study addresses the diffusion of oxygen in a spherical geometry with simultaneous absorption at a constant rate. The analytical method assumes a polynomial representation of the oxygen concentration profile, leading to a system of differential equations through mathematical manipulation. A nume...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/1/4 |
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| author | Soumaya Belabbes Abdellatif Boureghda |
| author_facet | Soumaya Belabbes Abdellatif Boureghda |
| author_sort | Soumaya Belabbes |
| collection | DOAJ |
| description | This study addresses the diffusion of oxygen in a spherical geometry with simultaneous absorption at a constant rate. The analytical method assumes a polynomial representation of the oxygen concentration profile, leading to a system of differential equations through mathematical manipulation. A numerical scheme is then employed to solve this system, linking the moving boundary and its velocity to determine the unknown functions within the assumed polynomial. An approximate analytical solution is obtained and compared with other methods, demonstrating very good agreement. This approach provides a novel method for addressing oxygen diffusion in spherical geometries, combining analytical techniques with numerical computations to efficiently solve for oxygen concentration profiles and moving boundary dynamics. |
| format | Article |
| id | doaj-art-de08584d30e24bb884aa3b966715e7f5 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-de08584d30e24bb884aa3b966715e7f52025-01-24T13:22:07ZengMDPI AGAxioms2075-16802024-12-01141410.3390/axioms14010004Numerical Solution of Oxygen Diffusion Problem in Spherical CellSoumaya Belabbes0Abdellatif Boureghda1Laboratory of Fundamental and Numerical Mathematics, Faculty of Sciences, Ferhat Abbas University, Sétif 19137, AlgeriaLaboratory of Fundamental and Numerical Mathematics, Faculty of Sciences, Ferhat Abbas University, Sétif 19137, AlgeriaThis study addresses the diffusion of oxygen in a spherical geometry with simultaneous absorption at a constant rate. The analytical method assumes a polynomial representation of the oxygen concentration profile, leading to a system of differential equations through mathematical manipulation. A numerical scheme is then employed to solve this system, linking the moving boundary and its velocity to determine the unknown functions within the assumed polynomial. An approximate analytical solution is obtained and compared with other methods, demonstrating very good agreement. This approach provides a novel method for addressing oxygen diffusion in spherical geometries, combining analytical techniques with numerical computations to efficiently solve for oxygen concentration profiles and moving boundary dynamics.https://www.mdpi.com/2075-1680/14/1/4oxygen diffusionabsorptionmoving boundary problemsStefan problemspartial differential equationsboundary conditions |
| spellingShingle | Soumaya Belabbes Abdellatif Boureghda Numerical Solution of Oxygen Diffusion Problem in Spherical Cell Axioms oxygen diffusion absorption moving boundary problems Stefan problems partial differential equations boundary conditions |
| title | Numerical Solution of Oxygen Diffusion Problem in Spherical Cell |
| title_full | Numerical Solution of Oxygen Diffusion Problem in Spherical Cell |
| title_fullStr | Numerical Solution of Oxygen Diffusion Problem in Spherical Cell |
| title_full_unstemmed | Numerical Solution of Oxygen Diffusion Problem in Spherical Cell |
| title_short | Numerical Solution of Oxygen Diffusion Problem in Spherical Cell |
| title_sort | numerical solution of oxygen diffusion problem in spherical cell |
| topic | oxygen diffusion absorption moving boundary problems Stefan problems partial differential equations boundary conditions |
| url | https://www.mdpi.com/2075-1680/14/1/4 |
| work_keys_str_mv | AT soumayabelabbes numericalsolutionofoxygendiffusionprobleminsphericalcell AT abdellatifboureghda numericalsolutionofoxygendiffusionprobleminsphericalcell |