Modeling heat transfer from a vertical isothermal plate using one-dimensional turbulence stochastic mixing model of turbulence

A turbulent natural convection boundary layer along a vertical isothermal flat plate in air is investigated based on the one-dimensional turbulence (ODT) modeling approach of Kerstein. The advantage of this approach is that near-wall conduction process can be treated without approximation. The effects of multi-dimensional turbulent mixing processes are modeled using a stochastic process description via triplet mapping stirring events. Adapting the ODT model to the problem of an isothermal plate includes modifying the local characteristic eddy time scale to account for the effects of buoyancy induced mixing mechanisms. Both a Lagrangian and Eulerian implementations of the ODT model are presented. Profiles of time-averaged and RMS velocity and temperature are compared to experimental data and existing self-similarity theory for thermal boundary layer along with Nusselt number predictions.