The Impact of Inclined Magnetic Field on Streamlines in a Constricted Lid-Driven Cavity
Yıl 2024,
Cilt: 28 Sayı: 1, 108 - 116, 29.02.2024
Merve Gürbüz Çaldağ
,
Ebutalib Çelik
Öz
The influence of oriented magnetic field on the incompressible and electrically conducting flow is investigated in a square cavity with a moving top wall and a no-slip constricted bottom wall. Radial basis function (RBF) approximation is employed to velocity-stream function-vorticity formulation of MHD equations. Numerical results are shown in terms of streamlines for different values of Hartmann number M, orientation angle of magnetic field θ and the height of the constricted bottom wall hc with a fixed Reynolds number. It is obtained that the number of vortices arises as either hc or M increases. However, the increase in θ leads to decrease the number of vortices. Formation of vortices depends on not only the strength and the orientation of the magnetic field but also the constriction of the bottom wall.
Kaynakça
- [1] C. Saidi, F. Legay-Desesquelles, B. Prunet-Foch, “Laminar flow past a sinusoidal cavity”, International Journal of Heat and Mass Transfer, vol. 30, no. 4, pp. 649–661, 1987.
- [2] P. K. Das, S. Mahmud, “Numerical investigation of natural convection inside a wavy enclosure”, International Journal of Thermal Sciences, vol. 42, no. 4, pp. 397–406, 2003.
- [3] G. C. Layek, C. Midya, “Effect of constriction height on flow separation in a two-dimensional channel”, Communications in Nonlinear Science and Numerical Simulation, vol. 12, no. 5, pp. 745–759, 2007.
- [4] E. Abu-Nada, H. F. Oztop, “Numerical analysis of Al2O3/water nanofluids natural convection in a wavy walled cavity”, Numerical Heat Transfer, Part A: Applications, vol. 59, no. 5, pp. 403–419, 2011.
- [5] S. Mekroussi, D. Nehari, M. Bouzit, N. E. S. Chemloul, “Analysis of mixed convection in an inclined lid-driven cavity with a wavy wall”, Journal of Mechanical Science and Technology, vol. 27, pp. 2181–2190, 2013.
- [6] E. B. Öğüt, M. Akyol, M. Arıcı, “Natural convection of nanofluids in an inclined square cavity with side wavy walls”, Isı Bilimi ve Tekniği Dergisi, vol. 37, no. 2, pp. 139–149, 2017.
- [7] F. M. Azizul, A. I. Alsabery, I. Hashim, A. J. Chamkha, “Heatline visualization of mixed convection inside double lid-driven cavity having heated wavy wall”, Journal of Thermal Analysis and Calorimetry, vol. 145, pp. 3159–3176, 2021.
- [8] M. Pirmohammadi, M. Ghassemi, “Effect of magnetic field on convection heat transfer inside a tilted square enclosure”, International Communications in Heat and Mass Transfer, vol. 36, no. 7, pp. 776–780, 2009.
- [9] H. F. Öztop, A. Sakhrieh, E. Abu-Nada, K. Al-Salem, “Mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure”, International Communications in Heat and Mass Transfer, vol. 86, pp. 42–51, 2017.
- [10] M. Tezer, M. Gürbüz, “MHD convection flow in a constricted channel”, Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica, vol. 26, no. 2, 2018.
- [11] W. H. Khalil, I. D. Azzawi, A. Al-damook, “The optimisation of MHD free convection inside porous trapezoidal cavity with the wavy bottom wall using response surface method”, International Communications in Heat and Mass Transfer, vol. 134, p. 106035, 2022.
- [12] T. Saha, T. Islam, S. Yeasmin, N. Parveen, “Thermal influence of heated fin on MHD natural convection flow of nanofluids inside a wavy square cavity”, International Journal of Thermofluids, vol. 18, p. 100338, 2023.
- [13] S. H. Aydın, H. Selvitopi, “Stabilized FEM-BEM coupled solution of MHD pipe flow in an unbounded conducting medium”, engineering anlaysis with boundary Elements, vol. 87, pp. 122-132, 2018.
- [14] K. Kaladhar, K. M. Reddy, D. Srinivasacharya, “Inclined magnetic field and soret effects on mixed convection flow between vertical parallel plates”, Journal of Applied Analysis and Computation, vol. 9, no. 6, pp. 2111–2123, 2019.
- [15] M. Wasif, K. A. Mishal, M. R. Haque, M. M. Haque, F. Rahman, “Investigation of fluid flow and heat transfer for an optimized lid driven cavity shape under the condition of inclined magnetic field”, Energy and Thermofluids Engineering, vol. 1, no. 1–2, pp. 47–57, 2021.
- [16] S. Hussain, H. F. Öztop, “Impact of inclined magnetic field and power law fluid on double diffusive mixed convection in lid-driven curvilinear cavity”, International Communications in Heat and Mass Transfer, vol. 127, p. 105549, 2021.
- [17] M. Gürbüz-Çaldağ, E. Çelik, “Stokes flow in lid-driven cavity under inclined magnetic field”, Archives of Mechanics, vol. 74, no. 6, 2022.
- [18] H. Selvitopi, “Numerical investigation of damped wave type MHD flow with time-varied external magnetic field”, Chinese Journal of Physics, vol. 80, pp. 127-147, 2022.
- [19] H. Selvitopi, “Stabilized FEM solution of magnetohydrodynamic flow in different geometries”, Journal of Scientific Reports-A, vol. 49, pp. 105-117, 2022.
- [20] 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, vol. 14, no. 10, pp. 1433–1444, 1959.
- [21] M. Gürbüz, M. Tezer-Sezgin, “MHD Stokes flow in lid-driven cavity and backward-facing step channel”, European Journal of Computational Mechanics, vol. 24, no. 6, pp. 279–301, 2015.
- [22] C. S. Chen, C. M. Fan, P. Wen, “The method of approximate particular solutions for solving certain partial differential equations”, Numerical Methods for Partial Differential Equations, vol. 28, no. 2, pp. 506–522, 2012.
- [23] M. Gürbüz, “Radial Basis Function and Dual Reciprocity Boundary Element Solutions of Fluid Dynamics Problems”, Ph.D. dissertation, Department of Mathematics, Middle East Technical University, Ankara, Türkiye, 2017.
- [24] U. Ghia, K. N. Ghia, C. Shin, “High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method”, Journal of Computational Physics, vol. 48, no. 3, pp. 387–411, 1982.
- [25] E. Çelik, M. Gürbüz-Çaldağ, “Streamline analysis of MHD flow in a double lid-driven cavity”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 238, pp. 64-74, 2024.
Yıl 2024,
Cilt: 28 Sayı: 1, 108 - 116, 29.02.2024
Merve Gürbüz Çaldağ
,
Ebutalib Çelik
Kaynakça
- [1] C. Saidi, F. Legay-Desesquelles, B. Prunet-Foch, “Laminar flow past a sinusoidal cavity”, International Journal of Heat and Mass Transfer, vol. 30, no. 4, pp. 649–661, 1987.
- [2] P. K. Das, S. Mahmud, “Numerical investigation of natural convection inside a wavy enclosure”, International Journal of Thermal Sciences, vol. 42, no. 4, pp. 397–406, 2003.
- [3] G. C. Layek, C. Midya, “Effect of constriction height on flow separation in a two-dimensional channel”, Communications in Nonlinear Science and Numerical Simulation, vol. 12, no. 5, pp. 745–759, 2007.
- [4] E. Abu-Nada, H. F. Oztop, “Numerical analysis of Al2O3/water nanofluids natural convection in a wavy walled cavity”, Numerical Heat Transfer, Part A: Applications, vol. 59, no. 5, pp. 403–419, 2011.
- [5] S. Mekroussi, D. Nehari, M. Bouzit, N. E. S. Chemloul, “Analysis of mixed convection in an inclined lid-driven cavity with a wavy wall”, Journal of Mechanical Science and Technology, vol. 27, pp. 2181–2190, 2013.
- [6] E. B. Öğüt, M. Akyol, M. Arıcı, “Natural convection of nanofluids in an inclined square cavity with side wavy walls”, Isı Bilimi ve Tekniği Dergisi, vol. 37, no. 2, pp. 139–149, 2017.
- [7] F. M. Azizul, A. I. Alsabery, I. Hashim, A. J. Chamkha, “Heatline visualization of mixed convection inside double lid-driven cavity having heated wavy wall”, Journal of Thermal Analysis and Calorimetry, vol. 145, pp. 3159–3176, 2021.
- [8] M. Pirmohammadi, M. Ghassemi, “Effect of magnetic field on convection heat transfer inside a tilted square enclosure”, International Communications in Heat and Mass Transfer, vol. 36, no. 7, pp. 776–780, 2009.
- [9] H. F. Öztop, A. Sakhrieh, E. Abu-Nada, K. Al-Salem, “Mixed convection of MHD flow in nanofluid filled and partially heated wavy walled lid-driven enclosure”, International Communications in Heat and Mass Transfer, vol. 86, pp. 42–51, 2017.
- [10] M. Tezer, M. Gürbüz, “MHD convection flow in a constricted channel”, Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica, vol. 26, no. 2, 2018.
- [11] W. H. Khalil, I. D. Azzawi, A. Al-damook, “The optimisation of MHD free convection inside porous trapezoidal cavity with the wavy bottom wall using response surface method”, International Communications in Heat and Mass Transfer, vol. 134, p. 106035, 2022.
- [12] T. Saha, T. Islam, S. Yeasmin, N. Parveen, “Thermal influence of heated fin on MHD natural convection flow of nanofluids inside a wavy square cavity”, International Journal of Thermofluids, vol. 18, p. 100338, 2023.
- [13] S. H. Aydın, H. Selvitopi, “Stabilized FEM-BEM coupled solution of MHD pipe flow in an unbounded conducting medium”, engineering anlaysis with boundary Elements, vol. 87, pp. 122-132, 2018.
- [14] K. Kaladhar, K. M. Reddy, D. Srinivasacharya, “Inclined magnetic field and soret effects on mixed convection flow between vertical parallel plates”, Journal of Applied Analysis and Computation, vol. 9, no. 6, pp. 2111–2123, 2019.
- [15] M. Wasif, K. A. Mishal, M. R. Haque, M. M. Haque, F. Rahman, “Investigation of fluid flow and heat transfer for an optimized lid driven cavity shape under the condition of inclined magnetic field”, Energy and Thermofluids Engineering, vol. 1, no. 1–2, pp. 47–57, 2021.
- [16] S. Hussain, H. F. Öztop, “Impact of inclined magnetic field and power law fluid on double diffusive mixed convection in lid-driven curvilinear cavity”, International Communications in Heat and Mass Transfer, vol. 127, p. 105549, 2021.
- [17] M. Gürbüz-Çaldağ, E. Çelik, “Stokes flow in lid-driven cavity under inclined magnetic field”, Archives of Mechanics, vol. 74, no. 6, 2022.
- [18] H. Selvitopi, “Numerical investigation of damped wave type MHD flow with time-varied external magnetic field”, Chinese Journal of Physics, vol. 80, pp. 127-147, 2022.
- [19] H. Selvitopi, “Stabilized FEM solution of magnetohydrodynamic flow in different geometries”, Journal of Scientific Reports-A, vol. 49, pp. 105-117, 2022.
- [20] 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, vol. 14, no. 10, pp. 1433–1444, 1959.
- [21] M. Gürbüz, M. Tezer-Sezgin, “MHD Stokes flow in lid-driven cavity and backward-facing step channel”, European Journal of Computational Mechanics, vol. 24, no. 6, pp. 279–301, 2015.
- [22] C. S. Chen, C. M. Fan, P. Wen, “The method of approximate particular solutions for solving certain partial differential equations”, Numerical Methods for Partial Differential Equations, vol. 28, no. 2, pp. 506–522, 2012.
- [23] M. Gürbüz, “Radial Basis Function and Dual Reciprocity Boundary Element Solutions of Fluid Dynamics Problems”, Ph.D. dissertation, Department of Mathematics, Middle East Technical University, Ankara, Türkiye, 2017.
- [24] U. Ghia, K. N. Ghia, C. Shin, “High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method”, Journal of Computational Physics, vol. 48, no. 3, pp. 387–411, 1982.
- [25] E. Çelik, M. Gürbüz-Çaldağ, “Streamline analysis of MHD flow in a double lid-driven cavity”, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 238, pp. 64-74, 2024.