Chaotic convection of viscoelastic fluids in porous media

Sheu, Long-Jye; Tam, Lap Mou; Chen, Juhn-Horng; Chen, Hsien-Keng; Lin, Kuang-Tai; Yuan, Kun

doi:10.1016/j.chaos.2006.07.050

Cited by 64 publications

(42 citation statements)

References 25 publications

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“…Thermal stability of a viscoelastic Walters B liquid saturating a porous anisotropic horizontal layer in the presence of a chemical reaction has been discussed by Postelnicu (2007). Chaotic convection of viscoelastic fluid saturating a porous medium has been analyzed by Sheu et al (2008).…”

Section: Introductionmentioning

confidence: 99%

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

et al. 2010

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The linear stability of Walters B viscoelastic fluid-saturated horizontal porous layer is examined theoretically when the walls of the porous layer are subjected to time-periodic temperature modulation. Three types of boundary temperature modulations are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held at constant temperature. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Rayleigh number and the corresponding wave number. The shift in critical Rayleigh number is calculated as a function of modulation frequency, viscoelastic parameter, and Prandtl number. The effect of all three types of modulations is found to be destabilizing as compared to the unmodulated system. This result is in contrast to the system with other types of fluids. Besides, the influence of physical parameters on the control of convective instability of the system is discussed.

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Section: Introductionmentioning

confidence: 99%

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

et al. 2010

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“…(4) As particular case, the present system reduces to the systems of Lorenz [9], Akhatov and Chembarisova [30], Sheu et al [31], and Khayat [26][27][28]. …”

Section: Journal Of Applied Mathematicsmentioning

confidence: 97%

“…Akhatov and Chemberisova [30] studied Rayleigh-Bénard convection in Oldroyd's fluid saturated porous layer with negligible Darcy effect and deduced a three-order autonomous chaotic system. Chaotic Rayleigh-Bénard convection in Oldroyd's fluid saturated porous medium using a thermal equilibrium model was investigated by Sheu et al [31]. Recently Bhadauria and Kiran [15] studied double diffusive chaotic and oscillatory magnetoconvection in a viscoelastic fluid under G-jitter and found that modulated gravity field can be used either to delay or enhance the heat and mass transfer in the system.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Convection in a Viscoelastic Fluid Saturated Porous Medium with a Heat Source

Bhadauria

2016

Journal of Applied Mathematics

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Chaotic convection in a viscoelastic fluid saturated porous layer, heated from below, is studied by using Oldroyd's type constituting relation and in the presence of an internal heat source. A modified Darcy law is used in the momentum equation, and a heat source term has been considered in energy equation. An autonomous system of fourth-order differential equations has been deduced by using a truncated Fourier series. Effect of internal heat generation on chaotic convection has been investigated. The asymptotic behavior can be stationary, periodic, or chaotic, depending upon the flow parameters. Construction of four-scroll, or "two-butterfly," and chaotic attractor has been examined.

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“…Let us consider a thermal convection in a viscoelastic fluidsaturated porous medium [1]. A model has been proposed in [1] resulting from the truncated Galerkin expansion to the momentum and heat transfer equations.…”

Section: A Integer-order System Of the Thermal Convection In A Viscomentioning

confidence: 99%

“…Modeling the thermal convection has attracted the interest of engineers and scientists for a long time due to its numerous applications [1]. Understanding of the thermal convective behavior is important for controlling processes like the utilization of geothermal energy such as building thermal insulation.…”

Section: Introductionmentioning

confidence: 99%

Chaotic convective behavior and stability analysis of a fractional viscoelastic fluids model in porous media

Ndoye

Laleg‐Kirati

2015

2015 3rd International Conference on Control, Engineering &Amp; Information Technology (CEIT)

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Abstract-In this paper, a dynamical fractional viscoelastic fluids convection model in porous media is proposed and its chaotic behavior is studied. A preformed equilibrium points analysis indicates the conditions where chaotic dynamics can be observed, and show the existence of chaos. The behavior and stability analysis of the integer-order and the fractional commensurate and non-commensurate orders of a fractional viscoelastic fluids system, which exhibits chaos, are presented as well.

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Chaotic convection of viscoelastic fluids in porous media

Cited by 64 publications

References 25 publications

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

Chaotic Convection in a Viscoelastic Fluid Saturated Porous Medium with a Heat Source

Chaotic convective behavior and stability analysis of a fractional viscoelastic fluids model in porous media

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