215
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Stabilizing subgrid FEM solution of the natural convection flow under high magnitude magnetic field on sinusoidal corrugated enclosure

&
Pages 420-430 | Received 31 Aug 2018, Accepted 19 Jun 2019, Published online: 07 Jul 2019

References

  • N. Alsoy Akgün and M. Tezer-Sezgin, DRBEM and DQM solutions of natural convection flow in a cavity under a magnetic field, Prog. Comput. Fluid Dyn. 13(5) (2013), pp. 270–284. doi: 10.1504/PCFD.2013.055056
  • S.H. Aydın, Two-level finite element method with a stabilizing subgrid for the natural convection flow simulation in different geometries, Numer. Heat Transfer A: Appl. 59 (2011), pp. 799–813. doi: 10.1080/10407782.2011.572764
  • S.H. Aydın, A.I. Neslitürk, and M. Tezer-Sezgin, Two-level finite element method with a stabilizing subgrid for the incompressible MHD equations, Int. J. Numer. Methods Fluids 62(2) (2010), pp. 188–210.
  • I. Babuska, The finite element method with Lagrangian multipliers, Numer. Math. 20 (1973), pp. 179–192. doi: 10.1007/BF01436561
  • F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrange multipliers, RAIRO Ser. Rouge 8 (1974), pp. 129–151.
  • A.N. Brooks and T.J.R. Hughes, Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Eng. 32 (1982), pp. 199–259. doi: 10.1016/0045-7825(82)90071-8
  • G.D.V. Davis and P. Jones, Natural convection in a square cavity: A comparison exercise, Int. J. Numer. Methods Fluids 3 (1983), pp. 227–248. doi: 10.1002/fld.1650030304
  • M. Dehghan and M. Abbaszadeh, Error analysis and numerical simulation of magnetohydrodynamics (MHD) equation based on the interpolating element free Galerkin (IEFG) method, Appl. Numer. Math. 137 (2019), pp. 252–273.doi:10.1016/j.apnum.2018.10.004
  • M. Dehghan and V. Mohammadi, The method of variably scaled radial kernels for solving two-dimensional magnetohydrodynamic (MHD) equations using two discretizations: The Crank–Nicolson scheme and the method of lines (MOL), Comput. Math. Appl. 70(10) (2015), pp. 2292–2315. doi: 10.1016/j.camwa.2015.08.032
  • M. Dehghan and M. Safarpoor, The dual reciprocity boundary elements method for the linear and nonlinear two-dimensional time-fractional partial differential equations, Math. Methods Appl. Sci. 39(14) (2016), pp. 3979–3995. doi: 10.1002/mma.3839
  • M. Dehghan and R. Salehi, A meshfree weak-strong (MWS) form method for the steady magnetohydrodynamic (MHD) flow in pipe with arbitrary wall conductivity, Comput. Mech. 52(6) (2013), pp. 1445–1462. doi: 10.1007/s00466-013-0886-z
  • L.P. Franca and F. Valentin, On an improved unusual stabilized finite element method for the advective-reactive-diffusive equation, Comput. Methods Appl. Mech. Eng. 190 (2000), pp. 1785–1800. doi: 10.1016/S0045-7825(00)00190-0
  • S. Gümgüm and M. Tezer-Sezgin, DRBEM solution of natural convection flow of nanofluids with a heat source, Eng. Anal. Bound. Elem. 34 (2010), pp. 727–737. doi: 10.1016/j.enganabound.2010.03.006
  • S. Gümgüm and M. Tezer-Sezgin, DRBEM solution of natural convective flow of micropolar fluids, Numer. Heat Transfer A: Appl. 57(10) (2010), pp. 777–798. doi: 10.1080/10407781003800680
  • H. Hosseinzadeh, M. Dehghan, and D. Mirzaei, The boundary elements method for magneto-hydrodynamic (MHD) channel flows at high Hartmann numbers, Appl. Math. Model. 37 (2013), pp. 2337–2351. doi: 10.1016/j.apm.2012.05.020
  • T.J.R. Hughes, Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, Comput. Methods Appl. Mech. Eng. 127(1–4) (1995), pp. 387–401. doi: 10.1016/0045-7825(95)00844-9
  • T.J.R. Hughes, G.R. Feijo, L. Mazzei, and J.B. Quincy, The variational multiscale method – a paradigm for computational mechanics, Comput. Methods Appl. Mech. Eng. 166(1–2) (1998), pp. 3–24. doi: 10.1016/S0045-7825(98)00079-6
  • S.H. Hussain, A.K. Hussein, and R.N. Mohammed, Studying the effects of a longitudinal magnetic field and discrete isoflux heat source size on natural convection inside a tilted sinusoidal corrugated enclosure, Comput. Math. Appl. 64 (2012), pp. 476–488. doi: 10.1016/j.camwa.2011.12.022
  • H.M. Metwally and R.M. Manglik, Enhanced heat transfer due to curvature-induced lateral vortices in laminar flows in sinusoidal corrugated-plate channels, Int. J. Heat Mass Transfer 47 (2004), pp. 2283–2292. doi: 10.1016/j.ijheatmasstransfer.2003.11.019
  • B. Pekmen and M. Tezer-Sezgin, DRBEM Solution of natural convective heat transfer with a non-Darcy model in a porous medium, J. Math. Chem. 53(3) (2015), pp. 911–924. doi: 10.1007/s10910-014-0448-4
  • J.N. Reddy, An Introduction to the Finite Element Method, McGraw-Hill, New York, 1993.
  • C. Shu and K.H.A. Wee, Numerical simulation of natural convection in a square cavity by SIMPLE-generalized differential quadrature method, Comput. Fluids 31 (2002), pp. 209–226. doi: 10.1016/S0045-7930(01)00024-X
  • M. Tezer-Sezgin, Boundary element methods solution MHD flow in a rectangular duct, Int. J. Numer. Methods Fluids 18 (1994), pp. 937–952. doi: 10.1002/fld.1650181004
  • M. Tezer-Sezgin and C. Bozkaya, Boundary element method solution of magnetohydrodynamic flow in a rectangular duct with conducting walls parallel to applied magnetic field, Comput. Mech. 41 (2008), pp. 769–775. doi: 10.1007/s00466-006-0139-5
  • M. Tezer-Sezgin and S. Han Aydin, Solution of magnetohydrodynamic flow problems using the boundary element method, Eng. Anal. Bound. Elem. 30 (2006), pp. 411–418. doi: 10.1016/j.enganabound.2005.12.001
  • Ö. Türk and M. Tezer-Sezgin, FEM solution of natural convection flow in square enclosures under magnetic field, Int. J. Numer. Methods Heat Fluid Flow 23(5) (2013), pp. 844–866. doi: 10.1108/HFF-12-2010-0196

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.