Generalized Lorenz Equation Derived from Thermal Convection of Viscoelastic Fluids in a Loop

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.