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Chaotic convection of viscoelastic fluids in porous media

Author

Listed:
  • Sheu, Long-Jye
  • Tam, Lap-Mou
  • Chen, Juhn-Horng
  • Chen, Hsien-Keng
  • Lin, Kuang-Tai
  • Kang, Yuan

Abstract

Buoyancy-induced convection in a viscoelastic fluid-saturated porous medium was analyzed using an Oldroydian-type constitutive relation. An autonomous system with four differential equations was deduced by applying the truncated Galerkin expansion to the momentum and heat transfer equations. The four-dimensional system can be reduced to many systems provided in the literature such as the Lorenz system, Vadasz system, Khayat system, and Akhatov system. Depending on the flow parameters, the asymptotic behavior can be stationary, periodic, or chaotic. Generation of a four-scroll, or two-“butterfly”, chaotic attractor was observed. Results also show that stress relaxation tends to precipitate the onset of chaos.

Suggested Citation

  • Sheu, Long-Jye & Tam, Lap-Mou & Chen, Juhn-Horng & Chen, Hsien-Keng & Lin, Kuang-Tai & Kang, Yuan, 2008. "Chaotic convection of viscoelastic fluids in porous media," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 113-124.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:1:p:113-124
    DOI: 10.1016/j.chaos.2006.07.050
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    1. Sheu, Long-Jye, 2006. "An autonomous system for chaotic convection in a porous medium using a thermal non-equilibrium model," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 672-689.
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    Cited by:

    1. Alkharashi, Sameh A., 2019. "A model of two viscoelastic liquid films traveling down in an inclined electrified channel," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 553-575.

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