低Pr数流体非稳态自然对流流动的标度分析

施加了恒定热通量的竖直平板置于静止的均匀或线性分层流体中会在板壁上形成自然对流流 动. 它在达到稳态前将先历经起始和过渡两个阶段. 而表征其瞬时流动特征的主要参数是壁温、热边界层厚度、内层和外层速度边界层厚度、边界层内竖直方向的最大速度、以及层流边界层发展达到稳态所需的时间. 利用标度分析得到了均匀和线性分层低普郎特数(Pr<1)流体沿恒定热通量竖直平板的非稳态自然对流流动在各个发展阶段的标度关系.

SCALING ANALYSIS OF UNSTEADY NATURAL CONVECTION FLOW OF A FLUID WITH LOW PRANDTL NUMBER

A natural convection flow will be formed adjacent to a vertical plane immersed in a quiescent homogeneous or linearly-stratified fluid after the plate is heated with a uniform thermal flux. The flow will undergo a start-up stage, followed by a transitional stage, before reaching a steady state. The transient behavior of the flow is parameterized by the plate temperature, the thermal boundary-layer thickness, the inner and outer velocity boundary-layer thicknesses, the maximum vertical velocity within the boundary layer, and the time for the boundary layer to reach the steady state. In this paper, a scaling analysis is used to obtain scaling laws for all the parameters at various development stages of unsteady natural convection boundary-layer flow in homogeneous and linearly-stratified fluids with low Prandtl number ($Pr<1$) along a vertical plate heated with a uniform thermal flux.