Prandtl number scaling of natural convection of an inclined flat plate due to uniform surface heat flux

Abstract

A new scaling analysis has been performed for the unsteady natural convection boundary layer under a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages including an early stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as numerical results. Earlier scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings performed very well with Rayleigh number and aspect ratio dependency. In this study, a modified Prandtl number scaling has been developed using a triple-layer integral approach for $Pr > 1$. It is seen that in comparison to the direct numerical simulations, the new scaling performs considerably better than the previous scaling.