A unified system describing dynamics of chaotic convection

Sheu, Long Jye; Chen, Juhn Horng; Chen, Hsien Keng; Tam, Lap Mou; Chao, Yi

doi:10.1016/j.chaos.2007.11.017

Cited by 17 publications

(9 citation statements)

References 28 publications

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“…The works on convective instability thresholds for viscoelastic fluids in porous media [18][19][20][21][22][23][24] can be found in the literature and have not been given much attention. The works on convective instability thresholds for viscoelastic fluids in porous media [18][19][20][21][22][23][24] can be found in the literature and have not been given much attention.…”

Section: Introductionmentioning

confidence: 99%

The onset of double diffusive convection in a binary Maxwell fluid saturated porous layer with cross-diffusion effects

Malashetty

Biradar

2011

Physics of Fluids

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The onset of double diffusive convection in a binary Maxwell fluid saturated porous layer with cross diffusion effects is studied using linear and weakly nonlinear stability analyses. The modified Darcy-Maxwell model is used for the momentum equation. The onset criterion for stationary and oscillatory convection is derived analytically. There is a competition between the processes of viscoelasticity and diffusions that causes the convection to set in through oscillatory rather than stationary. The effect of relaxation parameter, Dufour and Soret parameters, Lewis number, solute Rayleigh number, Vadasz number, and normalized porosity parameter on the stability of the system is investigated. The nonlinear theory based on the truncated representation of Fourier series method is used to find the heat and mass transfer. The effect of various parameters on transient heat and mass transfer is also brought out. PHYSICS OF FLUIDS 23, 064109 (2011) Downloaded 18 Sep 2013 to 130.240.43.43. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions 064109-2 M. S. Malashetty and B. S. Biradar Phys. Fluids 23, 064109 (2011) Downloaded 18 Sep 2013 to 130.240.43.43. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://pof.aip.org/about/rights_and_permissions

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Section: Introductionmentioning

confidence: 99%

The onset of double diffusive convection in a binary Maxwell fluid saturated porous layer with cross-diffusion effects

Malashetty

Biradar

2011

Physics of Fluids

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“…A qualitative expression of the Nusselt number when the system is out of equilibrium was derived. Sheu et al (2009) investigated chaotic thermal convection in an Oldroydian fluid-saturated porous medium using a thermal non-equilibrium model. There are some studies on convection in binary viscoelastic fluid-saturated porous media.…”

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confidence: 99%

Thermal Instability in a Porous Medium Layer Saturated with a Viscoelastic Nanofluid

Sheu

2011

Transp Porous Med

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The onset of convection in a horizontal layer of a porous medium saturated with a viscoelastic nanofluid was studied in this article. The modified Darcy model was applied to simulate the momentum equation in porous media. An Oldroyd-B type constitutive equation was used to describe the rheological behavior of viscoelastic nanofluids. The model used for the viscoelastic nanofluid incorporates the effects of Brownian motion and thermophoresis. The onset criterion for stationary and oscillatory convection was analytically derived. The effects of the concentration Rayleigh number, Prandtl number, Lewis number, capacity ratio, relaxation, and retardation parameters on the stability of the system were investigated. Oscillatory instability is possible in both bottom-and top-heavy nanoparticle distributions. Results indicated that there is competition among the processes of thermophoresis, Brownian diffusion, and viscoelasticity that causes the convection to set in through oscillatory rather than stationary modes. Regimes of stationary and oscillatory convection for various parameters were derived and are discussed in detail.

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“…For this reason, current interest in this area is concerned with studies of the various viscoelastic models such as Maxwell fluids (Sokolov and Tanner [18]), Oldroyd type models (Eltayeb [19], Khayat [20], Siddheshwar et al [21]), Rivlin-Ericksen fluids (Siddheshwar [22], Siddheshwar and Srikrishna [23]) and Walters-B liquids (El-Sayed [24]). Analogous studies on viscoelastic fluid convection in porous media are those by Siddheshwar and Srikrishna [25], Shekar and Jayalatha [26], Kim et al [27], Tan and Masuoka [28], Sheu [29,30] and Shivakumara et al [31]. Awad et al [32] very recently studied double diffusive convection in Newtonian liquids (see also references therein) and analogous problems in porous media were studied by Wang and Tan [33].…”

Section: Rsmentioning

confidence: 92%

Linear and nonlinear stability analysis of binary Maxwell fluid convection in a porous medium

et al. 2011

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The stability analysis of the quiescent state in a Maxwell fluid-saturated densely packed porous medium subject to vertical concentration and temperature gradients is presented. A single phase model with local thermal equilibrium between the porous matrix and the Maxwell fluid is assumed. The critical Darcy-Rayleigh numbers and the corresponding wave numbers for the onset of stationary and oscillatory convection are determined. A Lorenz like system is obtained for weakly nonlinear stability analysis.

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A unified system describing dynamics of chaotic convection

Cited by 17 publications

References 28 publications

The onset of double diffusive convection in a binary Maxwell fluid saturated porous layer with cross-diffusion effects

The onset of double diffusive convection in a binary Maxwell fluid saturated porous layer with cross-diffusion effects

Thermal Instability in a Porous Medium Layer Saturated with a Viscoelastic Nanofluid

Linear and nonlinear stability analysis of binary Maxwell fluid convection in a porous medium

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