School of Ocean Science and Technology, Dalian University of Technology, Dalian, 116024, China.
Phys Rev E. 2019 Oct;100(4-1):043112. doi: 10.1103/PhysRevE.100.043112.
The transient convective boundary layer flow induced by heating an initially isothermal and stationary fluid with a linearly heated semi-infinite vertical plate is comprehensively investigated by a scaling analysis in the present study. The local temperature at the leading edge of the specified linear thermal profile can be any value that is no lower than the ambient fluid, which significantly differentiates the present study from previous similar investigations. Additionally, the convective flow associated with both Pr<1 and Pr>1 (where Pr is the Prandtl number) fluids is analyzed and quantified. The derived scaling relations demonstrate that the dynamics of the Pr<1 and Pr>1 fluids are fundamentally different and the two flows are described by different sets of scaling laws. The study also shows that the convective boundary layer flow first experiences an initial growth state, and it eventually transits to a fully steady state after the leading edge effect has been completely convected away. It is further revealed that unlike the extensively studied homogenously heating problem which is featured by a one-dimensional initial growth state and a two-dimensional fully developed state, the present flow is consistently two-dimensional if a nonzero background temperature stratification presents. The derived scaling relations are validated against the direct numerical simulation results, and a good agreement is obtained.
本研究通过标度分析，全面研究了初始等温且静止的流体被线性加热的半无限垂直板所产生的瞬态对流边界层流动。指定线性热分布前缘处的局部温度可以是任何不低于环境流体的温度，这与以前的类似研究有显著区别。此外，还分析和量化了与 Pr<1 和 Pr>1（其中 Pr 是普朗特数）流体相关的对流流动。推导出的标度关系表明，Pr<1 和 Pr>1 流体的动力学性质截然不同，这两种流动由不同的标度定律描述。研究还表明，对流边界层流动首先经历初始增长状态，并且在前缘效应完全被对流带走后，最终过渡到完全稳定状态。进一步揭示的是，与广泛研究的均匀加热问题不同，均匀加热问题的特点是一维初始增长状态和二维完全发展状态，如果存在非零背景温度分层，则本流动始终是二维的。推导出的标度关系与直接数值模拟结果进行了验证，结果吻合良好。
