### Abstract

Original language | American English |
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Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

DOIs | |

State | Published - 13 Oct 2011 |

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**Thermal nonlinear oscillator in mixed convection.** / Martínez-Suástegui, L.; Treviño, C.; Cajas, J. C.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Thermal nonlinear oscillator in mixed convection

AU - Martínez-Suástegui, L.

AU - Treviño, C.

AU - Cajas, J. C.

PY - 2011/10/13

Y1 - 2011/10/13

N2 - A detailed numerical simulation is carried out for transient laminar flow opposing mixed convection in a downward vertical channel flow with both walls suddenly subjected to isothermal heat sources over a finite portion of the channel walls, by solving the unsteady two-dimensional Navier-Stokes and energy equations. The dynamical behavior of the system is influenced by, in addition to the geometrical parameters, three nondimensional parameters: the Reynolds, Richardson, and Prandtl numbers. Numerical experiments were performed for fixed values of the geometrical parameters, the Reynolds number (Re=100) and the Prandtl number (Pr=7). With variation in the value of the buoyancy (Richardson number), the nonlinear dynamical response of the system can reach (i) a stationary solution, (ii) a local and then a global periodic solution where the system executes self-sustained relaxation oscillations, or (iii) a solution in which the relaxation oscillation is destroyed leading to a chaotic state. In this study, bifurcations between different states, phase-space plots of the self-oscillatory system, characteristic times of temperature oscillations, and an exact description of the oscillations are presented quantitatively for a range of values of the buoyancy parameter. The results include the effects of the Reynolds and Prandtl numbers on the evolution of the different transitions. © 2011 American Physical Society.

AB - A detailed numerical simulation is carried out for transient laminar flow opposing mixed convection in a downward vertical channel flow with both walls suddenly subjected to isothermal heat sources over a finite portion of the channel walls, by solving the unsteady two-dimensional Navier-Stokes and energy equations. The dynamical behavior of the system is influenced by, in addition to the geometrical parameters, three nondimensional parameters: the Reynolds, Richardson, and Prandtl numbers. Numerical experiments were performed for fixed values of the geometrical parameters, the Reynolds number (Re=100) and the Prandtl number (Pr=7). With variation in the value of the buoyancy (Richardson number), the nonlinear dynamical response of the system can reach (i) a stationary solution, (ii) a local and then a global periodic solution where the system executes self-sustained relaxation oscillations, or (iii) a solution in which the relaxation oscillation is destroyed leading to a chaotic state. In this study, bifurcations between different states, phase-space plots of the self-oscillatory system, characteristic times of temperature oscillations, and an exact description of the oscillations are presented quantitatively for a range of values of the buoyancy parameter. The results include the effects of the Reynolds and Prandtl numbers on the evolution of the different transitions. © 2011 American Physical Society.

U2 - 10.1103/PhysRevE.84.046310

DO - 10.1103/PhysRevE.84.046310

M3 - Article

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

ER -