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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 the heat transfer coefficient  for different values of conductivity ratio .
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pone-0079956-g005: Variation of the critical Rayleigh number for stationary mode with the heat transfer coefficient for different values of conductivity ratio .

Mentions: The variation of conductivity ratio on the critical Rayleigh number for stationary mode with the heat transfer coefficient for different values of conductivity ratio is shown in Fig. 5. We find that the critical Rayleigh number is independent of for small values of , but for large , the critical Rayleigh number decreases with increasing . Moreover, for very large , the critical Rayleigh number is independent of . Thus, we can draw the conclusion that the presence of non-equilibrium of heat transfer between the viscoelastic fluid and solid make the system instable.


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 the heat transfer coefficient  for different values of conductivity ratio .
© Copyright Policy
Related In: Results  -  Collection

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

pone-0079956-g005: Variation of the critical Rayleigh number for stationary mode with the heat transfer coefficient for different values of conductivity ratio .
Mentions: The variation of conductivity ratio on the critical Rayleigh number for stationary mode with the heat transfer coefficient for different values of conductivity ratio is shown in Fig. 5. We find that the critical Rayleigh number is independent of for small values of , but for large , the critical Rayleigh number decreases with increasing . Moreover, for very large , the critical Rayleigh number is independent of . Thus, we can draw the conclusion that the presence of non-equilibrium of heat transfer between the viscoelastic fluid and solid make the system instable.

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