Scalings for unsteady natural convection boundary layer under time-varying heating flux in a small Prandtl number fluid

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

“…The dependence of δ vi on f n is also very similar to that of δ T . However, different from that for δ , confirming the scaling (30). The dependence of δ vi on s and f n , i.e., the scaling ( 25) and ( 26), is verified by the DNS results in Figure 9(c), which shows that for all Pr = 10 runs, the relation between ∕ δ δ vi vi s , and ∕ ∕ τ τ ( ˆ) vi s , 1 2 at the SUS is linear and can be quantified by the DNS results as follows:…”

“…We extended our study 11 to the case under the time‐dependent sinusoidal temperature heating condition 16 by conducting a similar scaling analysis to develop the corresponding scalings, which were also well verified by numerical results. In the past several years, we had continued the studies using similar scaling analysis and numerical simulations to derive various scaling laws for the unsteady NCBL flow under the sinusoidal heat flux or temperature for Pr 1 fluid and Pr < 1 fluid in both homogeneous and stratified ambient fluids 28–30 . There are also some other recent studies on the unsteady NCBL flow behavior subject to different time‐dependent sinusoidal temperature or heat flux for Newtonian and non‐Newtonian fluids, such as References [31–35].…”

“…In the present study, the studies of Reference [11,16,28,30,36] are extended to the unsteady NCBL flow of a Pr > 1 fluid on a vertical solid surface subject to a sinusoidal heating flux in a linearly stratified ambient. The significance to investigate the Pr > 1 fluids for the scenario considered in this study is due to their numerous occurrences in nature and in practical applications.…”

“…In the past several years, we had continued the studies using similar scaling analysis and numerical simulations to derive various scaling laws for the unsteady NCBL flow under the sinusoidal heat flux or temperature for Pr > 1 fluid and Pr < 1 fluid in both homogeneous and stratified ambient fluids. [28][29][30] There are also some other recent studies on the unsteady NCBL flow behavior subject to different timedependent sinusoidal temperature or heat flux for Newtonian and non-Newtonian fluids, such as References [31][32][33][34][35]. Zhao et al 17 studied the convective instability of NCBL flow during its transition to the turbulent regime by introducing time-dependent sinusoidal temperature perturbations.…”