Have a personal or library account? Click to login
Numerical Solution of Natural Convective Heat Transfer Under Magnetic Field Effect Cover

Numerical Solution of Natural Convective Heat Transfer Under Magnetic Field Effect

By: Serpil Şahin and  Hüseyin Demir  
Open Access
|Apr 2019

References

  1. 1. Amber I., O’Donovan T. S. (2017), A numerical simulation of heat transfer in an enclosure with a nonlinear heat source, Numerical Heat Transfer, Part A: Applications, 71(11), 1081–1093.10.1080/10407782.2017.1330093
  2. 2. Batchelor G. K. (1956), Steady laminar flow with closed streamlines at large Reynolds number, J. Fluid Mech., 1, 177–190.10.1017/S0022112056000123
  3. 3. Benjamin A. S., Denny V. E. (1979), On the convergence of numerical solutions for 2-D flows in a cavity at large Re, J. Comp. Physics, 33, 340–358.10.1016/0021-9991(79)90160-8
  4. 4. De Vahl Davis G. (1983), Natural convection of air in a square cavity: A bench mark numerical solution, Int. J. for Num. Meth. in Fluids, 3, 249–264.10.1002/fld.1650030305
  5. 5. Demir H. (2005), Numerical modeling of viscoelastic cavity driven flow using finite difference simulations, Appl. Math. and Comp., 166, 64–83.10.1016/j.amc.2004.04.107
  6. 6. Elder J. W. (1965), Laminar free convection in a vertical slot, J. Fluid Mech., 23, 77–98.10.1017/S0022112065001246
  7. 7. Emery A., Chi H., Dale J. (1971), Free convection through vertical plane layers of non-Newtonian power law fluids, ASME J. Heat Transfer, 93, 164–171.10.1115/1.3449778
  8. 8. Erturk E., Corke T. C. (2001), Boundary layer leading-edge receptivity to sound at incidence angles, Journal of Fluid Mechanics, 444, 383–407.10.1017/S0022112001005456
  9. 9. Erturk E., Corke T. C., Gökçöl C. (2005), Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers, J. Numer. Meth. Fluids, 48, 747–774.10.1002/fld.953
  10. 10. Erturk E., Haddad O. M., Corke T. C. (2004), Laminar incompressible flow past parabolic bodies at angles of attack, AIAA Journal, 42, 2254–2265.10.2514/1.4032
  11. 11. Gebhart B., Jaluria Y., Mahajan R. L., Sammakia B. (1988), Buoyancy induced flows and transport, Washington: Hemisphere.10.1115/1.3226555
  12. 12. Ghia U., Ghia K. N., Shin C. T. (1982), High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. Comp. Physics, 48, 387–411.10.1016/0021-9991(82)90058-4
  13. 13. Gunzburger M. D., Meir A. J., Peterson J. S. (1991), On the existence, uniqueness and finite element approximation of solutions of the equations of stationary, incompressible magnetohydro-dynamics, Math. Comput., 56, 523–563.10.1090/S0025-5718-1991-1066834-0
  14. 14. Hasler U., Schneebeli A., Schötzau D. (2004), Mixed finite element approximation of incompressible MHD problems based on weighted regularization, Appl. Numer. Math., 51, 19–45.10.1016/j.apnum.2004.02.005
  15. 15. He Y. N., Li, J. (2009), Convergence of three iterative methods based on the finite element discretization for the stationary Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 198, 1351–1359.10.1016/j.cma.2008.12.001
  16. 16. Hou S., Zou Q., Chen S., Doolen G., Cogley A.C. (1995), Simulation of cavity flow by the Lattice Boltzmann method, J. Comp. Physics, 118, 329–347.10.1006/jcph.1995.1103
  17. 17. Khader M. M. (2016), Shifted Legendre Collocation method for the flow and heat transfer due to a stretching sheet embedded in a porous medium with variable thickness, variable thermal conductivity and thermal radiation, Mediterr. J. Math., 13, 2319–2336.10.1007/s00009-015-0594-3
  18. 18. Liao S. J., Zhu J. M. (1996), A short note on higher-order stream function-vorticity formulation of 2-D steady state Navier-Stokes equations, Int. J. Numer. Methods Fluids, 22, 1–9.10.1002/(SICI)1097-0363(19960115)22:1<;1::AID-FLD314>3.0.CO;2-5
  19. 19. Rayleigh R. (1916), On convection currents in a horizontal layer of fluid, when the higher temperature is on the underside, Phil. Mag., Ser.6, 32, 529–546.10.1080/14786441608635602
  20. 20. Rubin S. G., Khosla P. K. (1981), N-S calculations with a coupled strongly implicit method, Computers and Fluids, 9, 163–180.10.1016/0045-7930(81)90023-2
  21. 21. Rudraiah N., Barron R. M., Venkatachalappa M., Subbaraya C. K. (1995), Effect of a magnetic field on free convection in a rectangular enclosure, Int. J. Engng Sci., 33, 1075–1084.10.1016/0020-7225(94)00120-9
  22. 22. Salah N. B., Soulaimani A., Habashi W. G. (2001), A finite element method for magnetohydrodynamics, Comput. Methods Appl. Mech. Engrg., 190, 5867–5892.10.1016/S0045-7825(01)00196-7
  23. 23. Schreiber R., Keller H. B. (1983), Driven cavity flows by efficient numerical techniques, J. Comp. Physics, 49, 310–333.10.1016/0021-9991(83)90129-8
  24. 24. Shenoy A. V. (1988), Natural convection heat transfer to viscoelastic fluids, Houston: Gulf.
  25. 25. Siddheshwar P. G., Ramachandramurthy V., Uma D. (2011), Rayleigh-Benard and Marangoni magnetoconvection in Newtonian liquid with thermorheological effects, Int. J. Engng Sci., 49, 1078–1094.10.1016/j.ijengsci.2011.05.020
  26. 26. Siginer D. A., Valenzuela-Rendon A. (1994), Natural convection of viscoelastic liquids, Proc. ASME Fluids Engineering Division Summer Meeting, Symposium, ASME FED, 179, 31–41.
  27. 27. Smith G. D. (1978), Numerical solution of partial differential equations by finite difference methods, Oxford University Pres.
  28. 28. Tennehill J. C., Anderson D. A., Pletcher R. H. (1997), Computational fluid mechanics and heat transfer, Taylor& Francis.
  29. 29. Venkatachalappa M., Younghae D., Sankar M. (2011), Effect of magnetic field on the heat and mass transfer in a vertical annulus, Int. J. Engng Sci., 49, 262–278.10.1016/j.ijengsci.2010.12.002
  30. 30. Wilkes J. O., Churehill S. W. (1966), The finite-difference computation of natural convection in a rectangular enclosure, AICHEJ, 12, 161–166.10.1002/aic.690120129
  31. 31. Xu H., He Y. N. (2013), Some iterative finite element methods for steady Navier-Stokes equations with different viscosities, J. Comput. Phys., 232, 136–152.10.1016/j.jcp.2012.07.020
DOI: https://doi.org/10.2478/ama-2019-0004 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
Language: English
Page range: 23 - 29
Submitted on: Aug 3, 2018
Accepted on: Mar 13, 2019
Published on: Apr 18, 2019
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2019 Serpil Şahin, Hüseyin Demir, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.