Thermal nonlinear oscillator in mixed convection

L. Martínez-Suástegui, C. Treviño, J. C. Cajas

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

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.
Original languageAmerican English
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
DOIs
StatePublished - 13 Oct 2011

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Mixed Convection
Nonlinear Oscillator
Prandtl number
convection
oscillators
Relaxation Oscillations
Richardson number
Reynolds number
oscillations
Buoyancy
buoyancy
Oscillation
Transient Flow
Channel Flow
Heat Source
channel flow
Laminar Flow
heat sources
Stationary Solutions
Navier-Stokes

Cite this

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title = "Thermal nonlinear oscillator in mixed convection",
abstract = "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. {\circledC} 2011 American Physical Society.",
author = "L. Mart{\'i}nez-Su{\'a}stegui and C. Trevi{\~n}o and Cajas, {J. C.}",
year = "2011",
month = "10",
day = "13",
doi = "10.1103/PhysRevE.84.046310",
language = "American English",
journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
issn = "1539-3755",
publisher = "American Physical Society",

}

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

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 13.10.2011.

Research output: Contribution to journalArticleResearchpeer-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.

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DO - 10.1103/PhysRevE.84.046310

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