Convective heat transport in a rotating fluid layer of infinite Prandtl number: Optimum fields and upper bounds on Nusselt number

2003 ◽  
Vol 67 (2) ◽  
Author(s):  
Nikolay K. Vitanov
Keyword(s):  
Nusselt Number ◽  
Prandtl Number ◽  
Heat Transport ◽  
Convective Heat ◽  
Fluid Layer ◽  
Upper Bounds ◽  
Rotating Fluid

Bounds on the convective heat transport in containers

2001 ◽  
Vol 431 ◽  
pp. 427-432 ◽  
Author(s):  
RODNEY A. WORTHING
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Heat Transport ◽  
Convective Heat ◽  
Upper Bounds ◽  
Vertical Heat ◽  
Vertical Heat Flux

Using the Hopf–Doering–Constantin decomposition, we derive upper bounds on the vertical heat flux in closed containers. It is found that the original bound of Doering & Constantin (1996) for Nusselt number as a function of Rayleigh number, Nu [ges ] √R/4, holds, at the very least, asymptotically as R → ∞ under reasonably diverse experimental settings.

scholarly journals Upper bounds on Nusselt number at finite Prandtl number

2016 ◽  
Vol 260 (4) ◽  
pp. 3860-3880 ◽  
Author(s):  
Antoine Choffrut ◽  
Camilla Nobili ◽  
Felix Otto
Keyword(s):  
Nusselt Number ◽  
Prandtl Number ◽  
Upper Bounds

scholarly journals Stellar Convection as a Low Prandtl Number Flow

1991 ◽  
Vol 130 ◽  
pp. 57-61
Author(s):  
Josep M. Massaguer
Keyword(s):  
Nusselt Number ◽  
Prandtl Number ◽  
Heat Transport ◽  
Large Scale ◽  
Shear Layers ◽  
Turbulent Convection ◽  
The Sun ◽  
Stellar Convection ◽  
Cool Stars ◽  
Number Flow

AbstractThermal convection in the Sun and cool stars is often modeled with the assumption of an effective Prandtl number σ ≃ 1. Such a parameterization results in masking of the presence of internal shear layers which, for small σ, might control the large scale dynamics. In this paper we discuss the relevance of such layers in turbulent convection. Implications for heat transport – i.e. for the Nusselt number power law – are also discussed.

The effects of significant viscosity variation on convective heat transport in water-saturated porous media

1982 ◽  
Vol 117 ◽  
pp. 233-249 ◽  
Author(s):  
J. Gary ◽  
D. R. Kassoy ◽  
H. Tadjeran ◽  
A. Zebib
Keyword(s):  
Porous Media ◽  
Nusselt Number ◽  
Finite Difference ◽  
Heat Transport ◽  
Convective Heat ◽  
Temperature Difference ◽  
Saturated Porous Media ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
Water Saturated

Weakly nonlinear theory and finite-difference calculations are used to describe steadystate and oscillatory convective heat transport in water-saturated porous media. Two-dimensional rolls in a rectangular region are considered when the imposed temperature difference between the horizontal boundaries is as large as 200 K, corresponding to a viscosity ratio of about 6·5. The lowest-order weakly nonlinear results indicate that the variation of the Nusselt number with the ratio of the actual Rayleigh number to the corresponding critical value R/Rc, is independent of the temperature difference for the range considered. Results for the Nusselt number obtained from finite-difference solutions contain a weak dependence on temperature difference which increases with the magnitude of R/Rc. When R/Rc = 8 the constantviscosity convection pattern is steady, while those with temperature differences of 100 and 200 K are found to oscillate.

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