Scaling analysis of unsteady natural convection boundary layers on an evenly heated plate with a time-dependent temperature

In this paper, a scaling analysis using a simple three-region structure was conducted for the unsteady natural convection boundary layer (NCBL) of a homogeneous Newtonian fluid with Pr > 1 adjacent to a vertical plate evenly heated with a time-dependent sinusoidal temperature. A series of scalings were developed for the thermal boundary thickness, the viscous boundary thicknesses, the maximum vertical velocity within the boundary layer, and the local and average Nusselt number across the plate, which are the major parameters representing the flow behavior, in terms of the governing parameters of the flow, i.e.the Rayleigh number Ra, the Prandtl number Pr, and the dimensionless natural frequency f(n) of the time-dependent sinusoidal temperature, at the start-up stage, at the transition time scale which represents the ending of the start-up stage and the beginning of the transitional stage of the boundary-layer development, and at the quasi-steady stage.

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AFMC 2014: 19th Australasian Fluid Mechanics Conference

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978-0-646-59695-2

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