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

Abstract

The unsteady natural convection boundary layer (NCBL) on a vertical wall heated by time-varying flux in initially quiescent homogeneous fluid with a small Prandtl number (Pr) was studied. Scalings for the parameters typifying NCBL behavior, including plate temperature, maximum vertical velocity, thermal boundary-layer thickness, and velocity boundary-layer thickness, at different development stages, and the time for the transition from the start-up stage to the quasi-steady state, were developed by scaling analysis. The obtained scalings were compared to and validated by the numerical results with different values of Pr, the Rayleigh number Ra and the dimensionless time-varying heat flux frequency fn, over 106 ≤ Ra ≤ 109, 0.01 ≤ Pr ≤ 0.5, and 0.001 ≤ fn ≤ 0.025. It is also found that the development of the boundary layer at the start-up stage is one-dimensional and but becomes two-dimensional at the quasi-steady state.