Prandtl number scalings for unsteady natural convection boundary-layer flow on an evenly heated vertical plate in a homogeneous Pr > 1 fluid

Abstract

Scalings for the thicknesses of the thermal and velocity boundary layers, the plate temperature, and the maximum vertical velocity in a homogeneous Pr > 1 fluid are validated against numerical results for unsteady natural convection boundary-layer flow on an evenly heated vertical plate. Results have been obtained for Rayleigh number ${10}^6\le \text{Ra}\le {10}^9$ and Prandtl number $3\le \text{Pr}\le 100,$ and the scaling relations are shown to provide a good description of the flow for both the initial conduction dominated, one-dimensional, unsteady phase and the fully developed convection dominated, two-dimensional, steady phase of the flow. Scaling constants have been obtained for all relations.

Additional information

Funding

The support from the Australian Research Council is gratefully acknowledged.