In this paper, a scaling analysis using a simple three-regionstructure was conducted for the unsteady natural convectionboundary layer (NCBL) of a homogeneous Newtonian fluidwith Pr > 1 adjacent to a vertical plate evenly heated with atime-dependent sinusoidal temperature. A series of scalingswere developed for the thermal boundary thickness, the viscousboundary thicknesses, the maximum vertical velocity withinthe boundary layer, and the local and average Nusselt numberacross the plate, which are the major parameters representingthe flow behavior, in terms of the governing parameters of theflow, i.e.the Rayleigh number Ra, the Prandtl number Pr, andthe dimensionless natural frequency fn of the time-dependentsinusoidal temperature, at the start-up stage, at the transitiontime scale which represents the ending of the start-up stage andthe beginning of the transitional stage of the boundary-layer development,and at the quasi-steady stage.
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