Heat Transfer Scaling Close to the Wall for Turbulent Channel Flows

Abstract

This work serves a twofold purpose of briefly reviewing the currently existing literature on the scaling of thermal turbulent fields and, in addition, proposing a new scaling framework and testing its applicability. An extensive set of turbulent scalar transport data for turbulent flow in infinitely long channels is obtained using a Lagrangian scalar tracking approach combined with direct numerical simulation of turbulent flow. Two cases of Poiseuille channel flow, with friction Reynolds numbers 150 and 300, and different types of fluids with Prandtl number ranging from 0.7 to 50,000 are studied. Based on analysis of this database, it is argued that the value and the location of the maximum normal turbulent heat flux are important scaling parameters in turbulent heat transfer. Implementing such scaling on the mean temperature profile for different fluids and Reynolds number cases shows a collapse of the mean temperature profiles onto a single universal profile in the near wall region of the channel. In addition, the profiles of normal turbulent heat flux and the root mean square of the temperature fluctuations appear to collapse on one profile, respectively. The maximum normal turbulent heat flux is thus established as a turbulence thermal scaling parameter for both mean and fluctuating temperature statistics.