论文标题
大部分比对流的热通量和壁剪应力
Heat Flux and Wall Shear Stress in Large Aspect-Ratio Turbulent Vertical Convection
论文作者
论文摘要
我们对大方面比对流进行了理论分析，该对流在热通量和壁剪应力之间产生两种关系，分别由Nusselt数字（$ \ text {nu} $）和剪切reynolds编号（$ \ \ \ text {re} _ _ text {re}_τ$）来衡量（$ \ text $ \ text $） （$ \ text {pr} $）：$ \ text {re}_τ^2 \ text {nu} = f（\ text {pr}）\ text {pr}^{ - 1} \ text {ra} \ text {pr}^{\ varepsilon} \ text {re}_τ$带有$ \ varepsilon = 1/3 $，用于$ \ text {pr} \ gg1 $和$ \ varepsilon = 1 $ for $ f text {pr} $ \ text {pr} $和$ c $是常数。这些关系意味着$ \ text {nu} \ about [c^2f（\ text {pr}）]^{1/3} \ text {pr}^{ - （1-2 \ varepsilon）/3} \ text {ra} $ \ text {re}_τ\ \ lot [f（\ text {pr}）/c]^{1/3} \ text {pr}^{ - （1+ \ varepsilon）/3} \ text {ra}^{ra}^{1/3} $ for High $ \ text {1/3} $。
We present a theoretical analysis of large aspect-ratio turbulent vertical convection that yields two relationships between heat flux and wall shear stress, measured respectively by the Nusselt number ($\text{Nu}$) and shear Reynolds number ($\text{Re}_τ$), in terms of the Rayleigh ($\text{Ra}$) and Prandtl numbers ($\text{Pr}$): $\text{Re}_τ^2 \text{Nu} = f(\text{Pr}) \text{Pr}^{-1} \text{Ra}$ in the high-$\text{Ra}$ limit and $\text{Nu} \approx C \text{Pr}^{\varepsilon} \text{Re}_τ$ with $\varepsilon=1/3$ for $\text{Pr} \gg1$ and $\varepsilon=1$ for $\text{Pr} \ll 1$, where $f(\text{Pr})$ is not a power law of $\text{Pr}$ and $C$ is a constant. These relationships imply $\text{Nu} \approx [C^2f(\text{Pr})]^{1/3} \text{Pr}^{-(1-2\varepsilon)/3} \text{Ra}^{1/3}$ and $\text{Re}_τ\approx[f(\text{Pr})/C]^{1/3}\text{Pr}^{-(1+\varepsilon)/3}\text{Ra}^{1/3}$ for high $\text{Ra}$.
