### Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations

#### Öz

#### Anahtar kelimeler

#### Tam metin:

PDF#### Referanslar

[1] Ece, M. C., Büyük, E. 2007. FEM solution of natural convection flow in square enclosures under magnetic field., Meccanica, 42, 435-449.

[2] Colaço, M. J., Dulikravich, G. S., Orlande, H.R.B. 2009. Magnetohydrodynamic simulations using radial basis functions. International Journal of Heat and Mass Transfer, 52, 5932-5939.

[3] Mramor, K., Vertnik, R., Sarler, B. 2013. Simulation of Natural Convection Influenced by Magnetic Field with Explicit Local Radial Basis Function Collocation Method. CMES: Computer Modeling in Engineering & Sciences, 92, 327-352.

[4] Oztop, H. F., Al-Salem, K., Pop, I. 2011. MHD Mixed Convection in a Lid-driven Cavity with Corner Heater. International Journal of Heat and Mass Transfer, 54, 3494-3504.

[5] Al-Salem, K., Öztop, H. F., Pop, I., Varol, Y. 2011. Effects of moving lid direction on MHD mixed convection in a linearly heated cavity. International Journal of Heat and Mass Transfer, 55, 1103-1112.

[6] Türk, Ö., Tezer-Sezgin, M. 2013. Natural convection flow under a magnetic field in an inclined square enclosure differentialy heated on adjacent walls. International Journal of Numerical Methods for Heat & Fluid Flow, 23, 844-866.

[7] Sarris, I. E., Zikos, G. K., Grecos, A. P., Vlachos, N. S. 2006. On the Limits of Validity of the Low Magnetic Reynolds Number Approximation in MHD Natural Convection Heat Transfer. Numerical Heat Transfer, Part B: Fundamentals, 50, 157-180.

[8] Şentürk, K., Tessarotto, M., Aslan, N. 2009. Numerical solutions of liquid metal flows by incompressible magneto-hydrodynamics with heat transfer. International Journal for Numerical Methods in Fluids, 60(2009), 1200-1221.

[9] Bozkaya, N., Tezer-Sezgin, M. 2011. The DRBEM solution of incompressible MHD flow equations. International Journal for Numerical Methods in Fluids, 67, 1264-1282.

[10] Codina, R., Hernández, N. 2011. Approximation of the Thermally Coupled MHD Problem Using a Stabilized Finite Element Method. Journal of Computational Physics, 230, 1281-1303.

[11] Pekmen, B., Tezer-Sezgin, M. 2015. DRBEM Solution of MHD Flow with Magnetic Induction and Heat Transfer. CMES: Computer Modeling in Engineering & Sciences, 105, 183-207.

[12] Sivakumar, R., Vimala S., Sekhar, T. V. S. 2015. Influence of Induced Magnetic Field on Thermal MHD Flow. Numerical Heat Transfer, Part A: Applications, 68, 797-811.

[13] Selimli, S., Recebli, Z. 2018. Impact of electrical and magnetic field on cooling process of liquid metal duct magnetohydrodynamic flow. Thermal Science, 22, 263-271.

[14] Ha, M. Y., Kim, I. K., Yoon, H. S., Yoon, K. S., Lee, J. R., Balachandar, S., Chun, H. H. 2002. Twodimensional and unsteady natural convection in a horizontal enclosure with a square body. Numerical Heat Transfer, Part A: Applications, 41, 183-210.

[15] Davidson, P. A. 2001. An Introduction to Magnetohydrodynamics. Cambridge University Press, Cambridge.

[16] Yu, P. X., Tian, Z. F., Ying A. Y., Abdou, M. A. 2017. Stream function-velocity-magnetic induction compact difference method for the 2D steady incompressible full magnetohydrodynamic equations. Computer Physics Communications, 219, 45-69.

[17] Hu, K., Ma, Y., Xu, J. 2017. Stable finite element methods preserving ÑB=0 exactly for MHD models. Numerische Mathematik, 135, 371-396.

[18] Brackbill, J. U., Barnes, D. C. 1980. The Effect of Nonzero ÑB on the numerical solution of the magnetohydrodynamic equations . Journal of Computational Physics, 35, 426-430.

[19] Salah, N. B., Soulaimani, A., Habashi, A. 2001. A finite element method for magnetohydrodynamics. Computer Methods in Applied Mechanics and Engineering, 190, 5867-5892.

[20] Gottlieb, D., Orszag, S. A. 1977. Numerical Analysis of Spectral Methods: Theory and Applications. SIAM, Philadelphia.

[21] Boyd, J. P. 2000. Chebyshev and Fourier Spectral Methods. Dover, New York.

[22] Trefethen, L. N. 2000. Spectral Methods in Matlab. SIAM, Philadelphia.

[23] Botella, O., Peyret, R. 1998. Computing singular solutions of the Navier-Stokes equations with the Chebyshev-collocation method. International Journal for Numerical Methods in Fluids, 36, 125-163.

[24] Botella, O., Peyret, R. 2001. Benchmark Spectral Results on the Lid-Driven Cavity Flow. Computers & Fluids, 27(4), 421-433.

[25] Peyret, R. 2002. Spectral Methods for Incompressible Viscous Flow. Springer-Verlag, New York.

[26] Heinrichs, W., Kattelans, T. 2008. A direct solver for the least-squares spectral collocation system on rectangular elements for the incompressible Navier-Stokes equations . Journal of Computational Physics, 227(9), 4776-4796.

[27] Auteri, F., Quartapelle, Vigevano, L. 2002. Accurate Spectral Solution of the Singular Driven Cavity Problem. Journal of Computational Physics, 180, 597-615.

This work is licensed under a Creative Commons Attribution 4.0 License.

e-ISSN: 1308-6529