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

A natural convection flow will be formed adjacent to a verticalplane immersed in a quiescent homogeneous or linearly-stratified fluid afterthe plate is heated with a uniform thermal flux. The flow will undergo astart-up stage, followed by a transitional stage, before reaching a steadystate. The transient behavior of the flow is parameterized by the platetemperature, the thermal boundary-layer thickness, the inner and outervelocity boundary-layer thicknesses, the maximum vertical velocity withinthe boundary layer, and the time for the boundary layer to reach the steadystate. 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 fluidswith low Prandtl number (Pr<1) along a vertical plate heated with a uniform thermal flux.