Numerical Investigation of the Fully Damped Wave-Type Magnetohydrodynamic Flow Problem
Magnetohydrodynamic (MHD) flow plays a crucial role in various applications, ranging from nuclear fusion devices to MHD pumps. The mathematical modeling of such flows involves convection–diffusion-type equations, with fluid velocity governed by the Navier–Stokes equations and the magnetic field dete...
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2024-11-01
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| author | Seda Demir Harun Selvitopi |
| author_facet | Seda Demir Harun Selvitopi |
| author_sort | Seda Demir |
| collection | DOAJ |
| description | Magnetohydrodynamic (MHD) flow plays a crucial role in various applications, ranging from nuclear fusion devices to MHD pumps. The mathematical modeling of such flows involves convection–diffusion-type equations, with fluid velocity governed by the Navier–Stokes equations and the magnetic field determined by Maxwell’s equations through Ohm’s law. Due to the complexity of these models, most studies on steady and unsteady MHD equations rely on numerical methods, as theoretical solutions are limited to specific cases. In this research, we propose a damped-wave-type mathematical model to describe fluid flow within a channel, taking into account both the velocity and magnetic field components. The model is solved numerically using the finite difference method for time discretization and the finite element method for spatial discretization. Numerical results are displayed graphically for different values of Hartmann numbers, and a detailed analysis and discussion of the solutions are provided. |
| format | Article |
| id | doaj-art-83731b735cb347f7bef6373fcd57c834 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-83731b735cb347f7bef6373fcd57c8342024-11-26T18:11:32ZengMDPI AGMathematics2227-73902024-11-011222347310.3390/math12223473Numerical Investigation of the Fully Damped Wave-Type Magnetohydrodynamic Flow ProblemSeda Demir0Harun Selvitopi1Department of Mathematics, Faculty of Science, Erzurum Technical University, 25100 Erzurum, TürkiyeDepartment of Mathematics, Faculty of Science, Erzurum Technical University, 25100 Erzurum, TürkiyeMagnetohydrodynamic (MHD) flow plays a crucial role in various applications, ranging from nuclear fusion devices to MHD pumps. The mathematical modeling of such flows involves convection–diffusion-type equations, with fluid velocity governed by the Navier–Stokes equations and the magnetic field determined by Maxwell’s equations through Ohm’s law. Due to the complexity of these models, most studies on steady and unsteady MHD equations rely on numerical methods, as theoretical solutions are limited to specific cases. In this research, we propose a damped-wave-type mathematical model to describe fluid flow within a channel, taking into account both the velocity and magnetic field components. The model is solved numerically using the finite difference method for time discretization and the finite element method for spatial discretization. Numerical results are displayed graphically for different values of Hartmann numbers, and a detailed analysis and discussion of the solutions are provided.https://www.mdpi.com/2227-7390/12/22/3473magnetohydrodynamic fluid flow problemfinite element methodfinite difference method |
| spellingShingle | Seda Demir Harun Selvitopi Numerical Investigation of the Fully Damped Wave-Type Magnetohydrodynamic Flow Problem Mathematics magnetohydrodynamic fluid flow problem finite element method finite difference method |
| title | Numerical Investigation of the Fully Damped Wave-Type Magnetohydrodynamic Flow Problem |
| title_full | Numerical Investigation of the Fully Damped Wave-Type Magnetohydrodynamic Flow Problem |
| title_fullStr | Numerical Investigation of the Fully Damped Wave-Type Magnetohydrodynamic Flow Problem |
| title_full_unstemmed | Numerical Investigation of the Fully Damped Wave-Type Magnetohydrodynamic Flow Problem |
| title_short | Numerical Investigation of the Fully Damped Wave-Type Magnetohydrodynamic Flow Problem |
| title_sort | numerical investigation of the fully damped wave type magnetohydrodynamic flow problem |
| topic | magnetohydrodynamic fluid flow problem finite element method finite difference method |
| url | https://www.mdpi.com/2227-7390/12/22/3473 |
| work_keys_str_mv | AT sedademir numericalinvestigationofthefullydampedwavetypemagnetohydrodynamicflowproblem AT harunselvitopi numericalinvestigationofthefullydampedwavetypemagnetohydrodynamicflowproblem |