Natural convection boundary-layer flow on an evenly heated vertical plate with time-varying heating flux in a stratified Pr < 1 fluid

Abstract

The transient natural convection boundary-layer flow adjacent to a vertical plate heated with a time-dependent heat flux in an initially linearly stratified ambient fluid with Prandtl number (Pr) smaller than one was studied. Scaling analysis was used to obtain the scaling relations for the main parameters characterizing the flow behavior in terms of Pr, s, and f_n at the four development stages, i.e., the startup, transitional, steady, and the decay stage, where s is the dimensionless temperature stratification parameter which represents the relative extent of the background stratification with respect to the temperature gradient across the plate and f_n is the dimensionless natural frequency of the time-dependent heat flux applied to the plate. These parameters include the plate temperature, maximum vertical velocity, thermal and viscous boundary-layer thicknesses, and the corresponding time scales. The direct numerical simulation results over $0.1\le s\le 100,0.01\le \text{Pr}\le 0.2$ and $0.001\le f_n\le 0.025$ show that these scaling relations provide a good representation of the flow behavior.

Additional information

Funding

This study is supported by the National Natural Science Foundation of China (No. 51469035) and the Australian Research Council (ARC).