Scaling laws for natural convection boundary layer of a Pr > 1 fluid on a vertical solid surface subject to a sinusoidal temperature in a linearly-stratified ambient fluid

Abstract

The understanding of the transient behavior of natural convection boundary layer (NCBL) on a heated vertical solid surface under various heating conditions is of fundamental significance and application importance. In this study, scalings for the parameters representing the behavior of unsteady NCBL flow of a linearly-stratified Pr > 1 fluid on a semi-infinite vertical solid surface heated with a time-varying sinusoidal temperature at different development stages are developed with a scaling analysis, in terms of Ra, Pr, s, and fn, which are the Rayleigh number, Prandtl number, stratification number, and frequency of the sinusoidal temperature, respectively. These scalings are validated and quantified with a series of numerical simulations over wide ranges of Ra, Pr, s, and fn. The frequency of the fluctuations experienced by the NCBL behavior at the transitional stage, due to the stratification of the ambient fluid, is also analyzed, and it is shown that the previously obtained scaling for the unsteady NCBL case with the constant heat flux heating condition is basically applicable for the current case, Ra and fn have additional effects as well due to the time-varying nature of the applied temperature.