Thermal convection in a nonlinear non-Newtonian magnetic fluid

Article English OPEN
Laroze, D. ; Pleiner, H. (2015)
  • Publisher: Elsevier B.V.
  • Journal: Communications in Nonlinear Science and Numerical Simulation, volume 26, issue 1-3, pages 167-183 (issn: 1007-5704)
  • Related identifiers: doi: 10.1016/j.cnsns.2015.01.002
  • Subject: Applied Mathematics | Numerical Analysis | Modelling and Simulation
    arxiv: Physics::Fluid Dynamics

We report theoretical and numerical results on thermal convection of a magnetic fluid in a viscoelastic carrier liquid. The viscoelastic properties are described by a general nonlinear viscoelastic model that contains as special cases the standard phenomenological constitutive equations for the stress tensor. In order to explore numerically the system we perform a truncated Galerkin expansion obtaining a generalized Lorenz system with ten modes. We find numerically that the system has stationary, periodic and chaotic regimes. We establish phase diagrams to identify the different dynamical regimes as a function of the Rayleigh number and the viscoelastic material parameters.
  • References (65)
    65 references, page 1 of 7

    [1] Cross MC, Hohenberg PC. Rev Mod Phys 1993;65:851.

    [2] Kolodner P. J Non-Newtonian Fluid Mech 1998;75:167.

    [3] Martinez-Mardones J, Tiemann R, Walgraef D. J Non-Newtonian Fluid Mech 2000;93:1.

    [4] Laroze D, Martinez-Mardones J, Perez-Garcia C. Int J Bifurcation Chaos 2005;15:3329.

    [5] Wang S, Tan WC. Phys Lett A 2008;372:3046.

    [6] Awad FG, Sibanda Sandile P, Motsa S. Appl Math Modell 2010;34:3509.

    [7] Kumar A, Bhadauria BS. Phys Fluids 2011;23:054101.

    [8] Wang S, Tan WC. Int J Heat Fluid Flow 2011;32:88.

    [9] Delenda N, Hirata SC, Ouarzazi MN. J Non-Newtonian Fluid Mech 2012;181-182:11.

    [10] Laroze D, Martinez-Mardones J, PĂ©rez LM. Int J Bifurcation Chaos 2010;20:235.

  • Related Research Results (1)
    Physics and Astronomy (2012)
  • Metrics
    No metrics available
Share - Bookmark