Reflections on a Penetration Theory of Turbulent Heat Transfer

TL;DR

This paper presents a modified penetration theory for turbulent heat transfer, emphasizing different time scales for momentum and thermal layers, and provides a method to determine the thermal wall layer thickness that aligns well with experimental data.

Contribution

It introduces a new approach to penetration theory by differentiating the time scales for momentum and thermal layers and offers a method to determine thermal wall layer thickness.

Findings

The theory correlates well with experimental data on thermal wall layer thickness.

The theory accurately predicts Nusselt numbers in turbulent heat transfer.

A new method for determining thermal wall layer thickness is developed.

Abstract

This paper discusses a modified penetration theory where the time scale for the momentum wall layer is based on the onset of ejections from the wall but the time scale for the thermal layer is based on the unsteady state diffusion of heat from the wall into the streamwise flow, not the renewal of heat from eddies penetrating the wall layer. A method for the determination of the thickness of the thermal wall layer has been developed. The theory correlates adequately experimental data for both the thickness of the thermal wall layer and the Nusselt number. Key words: Heat transfer, penetration theory, turbulence, time scales.