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The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer with non-equilibrium model.

Yang Z, Wang S, Zhao M, Li S, Zhang Q - PLoS ONE (2013)

Bottom Line: The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately.The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed.The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan, P.R. China.

ABSTRACT
The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.

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Variation of the critical Rayleigh number for stationary mode with wavenumber a for different values of the heat transfer coefficient H.
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pone-0079956-g003: Variation of the critical Rayleigh number for stationary mode with wavenumber a for different values of the heat transfer coefficient H.

Mentions: Figures 3 and 4 summarize these results, which show the effects of varying values of and on the critical Rayleigh number for stationary mode , respectively. It is quite clear from Fig. 3 that the value of for any chosen wavenumber increases with increasing the value of heat transfer coefficient . Furthermore, there exists a corresponding shift in the position of the minimum peak in Fig. 3 and 4. Moreover, the larger the heat transfer coefficient is, the faster the heat transfer enabling the viscoelastic fluid to attain greater percolation velocity. Therefore large heat transfer coefficient favors onset of convection. From Figs. 4, we observe that the effect of increasing decreases the minimum of the Rayleigh number for stationary mode, indicating that the effect of the porosity modified conductivity ratio is to advance the onset of convection.


The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer with non-equilibrium model.

Yang Z, Wang S, Zhao M, Li S, Zhang Q - PLoS ONE (2013)

Variation of the critical Rayleigh number for stationary mode with wavenumber a for different values of the heat transfer coefficient H.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3842928&req=5

pone-0079956-g003: Variation of the critical Rayleigh number for stationary mode with wavenumber a for different values of the heat transfer coefficient H.
Mentions: Figures 3 and 4 summarize these results, which show the effects of varying values of and on the critical Rayleigh number for stationary mode , respectively. It is quite clear from Fig. 3 that the value of for any chosen wavenumber increases with increasing the value of heat transfer coefficient . Furthermore, there exists a corresponding shift in the position of the minimum peak in Fig. 3 and 4. Moreover, the larger the heat transfer coefficient is, the faster the heat transfer enabling the viscoelastic fluid to attain greater percolation velocity. Therefore large heat transfer coefficient favors onset of convection. From Figs. 4, we observe that the effect of increasing decreases the minimum of the Rayleigh number for stationary mode, indicating that the effect of the porosity modified conductivity ratio is to advance the onset of convection.

Bottom Line: The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately.The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed.The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan, P.R. China.

ABSTRACT
The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.

Show MeSH
Related in: MedlinePlus