| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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Generalized Lorenz Equation Derived from Thermal Convection of Viscoelastic Fluids in a Loop |
| YANG Fan, ZHU Ke-Qin |
| Department of Engineering Mechanics, Tsinghua University, Beijing 100084 |
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| Cite this article: |
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YANG Fan, ZHU Ke-Qin 2010 Chin. Phys. Lett. 27 034601 |
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Abstract A new generalized Lorenz system is presented based on the thermal convection of Oldroyd-B fluids in a circular loop. Two non-dimensional parameters De1 (a measure of the fluid relaxation) and De2 (a measure of the fluid retardation) appear in the equation. Then we study this generalized Lorenz equation numerically and find that the values of De1 and De2 can greatly influence the behavior of the solution. The fluid relaxation De1 is found to precipitate the onset of periodic solution (limit cycle) in the system and impedes the onset of chaos while the fluid retardation (De2) tends to delay the onset of the periodic solution and precipitate the onset of chaos in the system.
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| Keywords:
46.35.+z
47.50.-d
47.52.+j
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Received: 10 October 2009
Published: 09 March 2010
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| PACS: |
46.35.+z
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(Viscoelasticity, plasticity, viscoplasticity)
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47.50.-d
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(Non-Newtonian fluid flows)
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47.52.+j
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(Chaos in fluid dynamics)
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