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Tytuł artykułu

Numerical solution of natural convective heat transfer under magnetic field effect

Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this study, non-Newtonian pseudoplastic fluid flow equations for 2-D steady, incompressible, the natural convective heat transfer are solved numerically by pseudo time derivative. The stability properties of natural convective heat transfer in an enclosed cavity region heated from below under magnetic field effect are investigated depending on the Rayleigh and Chandrasekhar numbers. Stability properties are studied, in particular, for the Rayleigh number from 10[indeks górny]4 to 10[indeks górny]6 and for the Chandrasekhar number 3, 5 and 10. As a result, when Rayleigh number is bigger than 10[indeks górny]6 and Chandrasekhar number is bigger than 10, the instability occurs in the flow domain. The results obtained for natural convective heat transfer problem are shown in the figures for Newtonian and pseudoplastic fluids. Finally, the local Nusselt number is evaluated along the bottom wall.
Rocznik
Strony
23--29
Opis fizyczny
Bibliogr. 31 poz., rys., tab., wykr.
Twórcy
  • Faculty of Arts and Sciences, Department of Mathematics, Amasya University, 05000, İpekköy, Amasya, Turkey
  • Faculty of Arts and Sciences, Department of Mathematics, Ondokuz Mayıs University, 55200, Atakum, Samsun, Turkey
Bibliografia
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  • 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.
  • 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.
  • 5. Demir H. (2005), Numerical modeling of viscoelastic cavity driven flow using finite difference simulations, Appl. Math. and Comp., 166, 64–83.
  • 6. Elder J. W. (1965), Laminar free convection in a vertical slot, J. Fluid Mech., 23, 77–98.
  • 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.
  • 8. Erturk E., Corke T. C. (2001), Boundary layer leading-edge receptivity to sound at incidence angles, Journal of Fluid Mechanics, 444, 383–407.
  • 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. Erturk E., Haddad O. M., Corke T. C. (2004), Laminar incompressible flow past parabolic bodies at angles of attack, AIAA Journal, 42, 2254–2265.
  • 11. Gebhart B., Jaluria Y., Mahajan R. L., Sammakia B. (1988), Buoyancy induced flows and transport, Washington: Hemisphere.
  • 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.
  • 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.
  • 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.
  • 15. He Y. N., Li, J. (2009), Convergence of three iterative methods based on the finite element discretization for the stationary NavierStokes equations, Comput. Methods Appl. Mech. Engrg., 198, 1351–1359.
  • 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.
  • 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.
  • 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.
  • 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.
  • 20. Rubin S. G., Khosla P. K. (1981), N-S calculations with a coupled strongly implicit method, Computers and Fluids, 9, 163–180.
  • 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.
  • 22. Salah N. B., Soulaimani A., Habashi W. G. (2001), A finite element method for magnetohydrodynamics, Comput. Methods Appl. Mech. Engrg., 190, 5867–5892.
  • 23. Schreiber R., Keller H. B. (1983), Driven cavity flows by efficient numerical techniques, J. Comp. Physics, 49, 310–333.
  • 24. Shenoy A. V. (1988), Natural convection heat transfer to viscoelastic fluids, Houston: Gulf.
  • 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.
  • 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. Smith G. D. (1978), Numerical solution of partial differential equations by finite difference methods, Oxford University Pres.
  • 28. Tennehill J. C., Anderson D. A., Pletcher R. H. (1997), Computational fluid mechanics and heat transfer, Taylor& Francis.
  • 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.
  • 30. Wilkes J. O., Churehill S. W. (1966), The finite-difference computation of natural convection in a rectangular enclosure, AICHEJ, 12, 161–166.
  • 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.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-2a2fa95b-aef0-49bd-8682-d3a66adca500
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