Stokes flow in lid-driven cavity under inclined magnetic field

• Autorzy: Gürbüz-Çaldag M. , Çelik E.

Identyfikatory

DOI

10.24423/aom.4013

• Języki publikacji: EN

Abstrakty

EN

Stokes flow in a lid-driven cavity under the effect of an inclined magnetic field is studied. The radial basis function (RBF) approximation is employed to the magnetohydrodynamic (MHD) equations which include Navier-Stokes equations of fluid dynamics and Maxwell’s equations of electromagnetics through Ohm’s law with the Stokes approximation. Numerical results are obtained for the moderate Hartmann number (0 ≤ M ≤ 80) and different angles of a magnetic field (0 ≤ α ≤ π). It is found that the increase in the Hartmann number causes the development of new vortices under the main flow due to the impact of a magnetic field. However, the type of the inclination angle (acute or obtuse) determines the location of the vortices.

Słowa kluczowe

EN

radial basis function; MHD; Stokes flow; inclination angle

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2022
• Tom: Vol. 74, nr 6
• Strony: 549--564
• Opis fizyczny: Bibliogr. 37 poz., rys., tab., wykr.

Twórcy

autor

Gürbüz-Çaldag M.

• Baskent University, Department of Management, Ankara, Turkey
• TED University, Department of Mathematics, Ankara, Turkey

autor

Çelik E.

• Çanakkale Onsekiz Mart University, Department of Computer Technologies, Çanakkale, Turkey

Bibliografia

• 1. U. Müller, M. Bühler, Magnetofluiddynamics in Channels and Containers, Springer, New York, 2001.
• 2. M. Tezer-Sezgin, S.H. Aydın, Dual reciprocity boundary element method for magnetohydrodynamic flow using radial basis functions, International Journal of Computational Fluid Dynamics, 16, 49–63, 2002.
• 3. M. Tezer-Sezgin, S.H. Aydın, Solution of magnetohydrodynamic flow problems using the boundary element method, Engineering Analysis with Boundary Elements, 30, 411–418, 2006.
• 4. C. Bozkaya, M. Tezer-Sezgin, Fundamental solution for coupled magnetohydrodynamic flow equations, Journal of Computational and Applied Mathematics, 203, 125–144, 2007.
• 5. S. Molokov, Fully developed liquid-metal flow in multiple rectangular ducts in a strong uniform magnetic field, European Journal of Mechanics B/Fluids, 12, 769–787, 1993.
• 6. X. Xiao, C.N. Kim, Effects of the magnetic field direction and of the cross-sectional aspect ratio on the mass flow rate of MHD duct flows, Fusion Engineering and Design, 151, 2020.
• 7. T.Q. Hua, J.S. Walker, MHD Flow in rectangular ducts with inclined non-uniform tranverse magnetic field, Fusion Engineering and Design, 27, 703–710, 1995.
• 8. M.P. Jeyanthi, S. Ganesh, Numerical solution of steady MHD duct flow in a square annulus duct under strong transverse magnetic field, International Journal of Ambient Energy, 43, 1, 2816–2823, 2020.
• 9. G.H.R. Kefayati, M. Gorji-Bandpy, H. Sajjadi, D.D. Ganji, Lattice Boltzmann simulation of MHD mixed convection in a lid-driven square cavity with linearly heated Wall, Scientia Iranica, Transactions B: Mechanical Engineering, 19, 1053–1065, 2012.
• 10. K. Jin, S.P. Vanka, B.G. Thomas, Three-dimensional flow in a driven cavity subjected to an external magnetic field, ASME Jounal of Fluids Engineering, 137, 071104, 2015.
• 11. P.X. Yu, J.X. Qiu, Q. Qin, Zhen F. Tian, Numerical investigation of natural convection in a rectangular cavity under different directions of uniform magnetic field, International Journal of Heat and Mass Transfer, 67, 1131–1144, 2013.
• 12. S. Hussain, H.F. Öztop, K. Mehmood, N. Abu-Hamdeh, Effects of inclined magnetic field on mixed convection in a nanofluid filled double lid-driven cavity with volumetric heat generation or absorption using finite element method, Chinese Journal of Physics, 56, 484–501, 2018.
• 13. C.C. Cho, Mixed convection heat transfer and entropy generation of Cu-water nanofluid in wavy-wall lid-driven cavity in presence of inclined magnetic field, International Journal of Mechanical Sciences, 151, 703–714, 2019.
• 14. S. Hussain, M. Jamal, B.P. Geridonmez, Impact of fins and inclined magnetic field in double lid-driven cavity with Cu-water nanofluid, International Journal of Thermal Sciences, 161, 106707, 2021.
• 15. D.L. Young, C.W. Chen, C.M. Fan, K. Murugesan, C.C. Tsai, The method of fundamental solutions for Stokes flow in a rectangular cavity with cylinders, European Journal of Mechanics B/Fluids, 24, 703–716, 2005.
• 16. C.W. Chen, D.L. Young, C.C. Tsai, K. Murugesan, The method of fundamental solutions for inverse 2D Stokes problems, Computational Mechanics, 37, 2–14, 2005.
• 17. D.L. Young, S.J. Jane, C.M. Fan, K. Murugesan, C.C. Tsai, The method of fundamental solutions for 2D and 3D Stokes problems, Journal of Computational Physics, 211, 1–8, 2006.
• 18. T.I. Eldho, D.L. Young, Solution of Stokes flow problem using dual reciprocity boundary element method, Journal of the Chinese Institute of Engineers, 24, 141–150, 2001.
• 19. C.A. Bustamante, H. Power, Y.H. Sua, W.F. Florez, A global meshless collocation particular solution method (integrated radial basis function) for two-dimensional Stokes flow problems, Applied Mathematical Modelling, 37, 4538–4547, 2013.
• 20. A. Deliceoglu, S.H. Aydın, Topological flow structures in an L-shaped cavity with horizontal motion of the upper lid, Journal of Computational and Applied Mathematics, 259, part B, 937–943, 2014.
• 21. E. Çelik, M. Luzum, A. Deliceoglu, Stokes flow in a Z-shaped cavity with moving upper lid, Karaelmas Science and Engineering Journal, 11, 1, 12–22, 2021.
• 22. S. Qian, H. Bau, Magneto-hydrodynamics based microfluidics, Mechanics Research Communications, 36, 10–21, 2009.
• 23. H. Yosinobu, T. Kakutani, Two-dimensional Stokes flow of an electrically conducting fluid in a uniform magnetic field, Journal of the Physical Society of Japan, 14, 1433–1444, 1959.
• 24. M. Gürbüz, M. Tezer-Sezgin, MHD Stokes flow and heat transfer in a lid-driven square cavity under horizontal magnetic field, Mathematical Methods in the Applied Sciences, 41, 2350–2359, 2018.
• 25. O. Türk, An MHD Stokes eigenvalue problem and its approximation by a spectral collocation method, Computers and Mathematics with Applications, 80, 2045–2056, 2020.
• 26. M.K. Prasad, T. Bucha, Magnetohydrodynamic effect on axisymmetric Stokes flow past a weakly permeable spheroid with a solid core, Archives of Mechanics, 73, 599–633, 2021.
• 27. D.J. Tritton, Physical Fluid Dynamics, 2nd ed., Oxford Science Publications, New York, 1988.
• 28. C.S. Chen, C.M. Fan, P.H. Wen, The method of approximate particular solutions for solving certain partial differential equations, Numerical Methods Partial Differential Equations, 28, 506–522, 2012.
• 29. P.P. Chinchapatnam, K. Djidjeli, P.B. Nair, Unsymmetric and symmetric meshless schemes for the unsteady convection-diffusion equation, Computer Methods in Applied Mechanics and Engineering, 195, 19–22, 2432–2453, 2006.
• 30. H. Power, V. Barraco, A Comparison analysis between unsymmetric and symmetric radial basis function collocation methods for the numerical solution of partial differential equations, Computers and Mathematics with Applications, 43, 3–5, 551–583, 2002.
• 31. E. Larsson, E., B. Fornberg, A numerical study of some radial basis function based solution methods for elliptic PDEs, Computers and Mathematics with Applications, 46, 5–6, 891–902, 2003.
• 32. Phani P. Chinchapatnam , K. Djidjeli, P.B. Nair, Radial basis function meshless method for the steady incompressible Navier–Stokes equations, International Journal of Computer Mathematics, 84, 10, 1509-1521, 2007.
• 33. R. Franke, Scattered data interpolation: tests of some method, Mathematics of Computation, 38, 157, 181–200, 1982.
• 34. J.G. Wanga, G.R. Liu, On the optimal shape parameters of radial basis functions used for 2-D meshless methods, Computer Methods in Applied and Mechanical Engineering, 191, 2611–2630, 2002.
• 35. M. Gürbüz, M. Tezer-Sezgin, MHD Stokes flow in lid-driven cavity and backwardfacing step channel, European Journal of Computational Mechanics, 24, 279–301, 2015.
• 36. P.N. Shankar, Slow Viscous Flows: Qualitative Features and Quantitative Analysis Using Complex Eigenfunction Expansions, Imperial College Press Publisher, London, 2007.
• 37. H.K. Moffatt, Viscous and resistive eddies near a sharp corner, Journal of Fluid Mechanics, 18, 1, 1–18, 1964.