SCALING ANALYSIS OF UNSTEADY NATURAL CONVECTION FLOW OF A FLUID WITH LOW PRANDTL NUMBER
低Pr数流体非稳态自然对流流动的标度分析

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.