Bounds on convection driven by internal heating
Bounds on convection driven by internal heating
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内部加热驱动的对流界限
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
F. Busse
中科院分区：
文献类型：
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作者：
Lu Lu;C. Doering;F. Busse
边界推导出的时空平均温度的Boussinesq近似的流体层之间的固定温度的水平边界均匀加热H在整个体积。分析进行了有限和无限普朗特数流体。虽然在纯传导状态下的平均温度为T_T_H，但对流增强了热传输，超过了降低温度的静态传导。下限的平均温度的层规模与所施加的热通量的大小，一个标度指数的任意普朗特数的情况下，另一个无限普朗特数模型。具体来说，它是在这里证明，在大的加热速率，对流是重要的，有限普朗特数流体和<$T <$c2H5/7的无限普朗特数流体的<$T <$c1H2/3。显式的前因子c1和c2的缩放界限计算以及。
Bounds are derived for the space–time averaged temperature 〈T〉 of a fluid layer in the Boussinesq approximation between fixed-temperature horizontal boundaries subject to uniform heating H throughout the volume. The analysis is carried out for both finite and infinite Prandtl number fluids. While the average temperature 〈T〉∼H in the purely conductive state, convection enhances the heat transport beyond static conduction reducing the temperature. Lower bounds to the average temperature of the layer scale with the magnitude of the imposed heat flux, with one scaling exponent for the arbitrary Prandtl number case and another for the infinite Prandtl number model. Specifically, it is proven here that at large heating rates where convection is important, 〈T〉⩾c1H2/3 for finite Prandtl number fluids and 〈T〉⩾c2H5/7 for infinite Prandtl number fluids. Explicit prefactors c1 and c2 for the scaling bounds are computed as well.