Turbulent heat transfer and temperature fluctuations in a field with uniform velocity and temperature gradients

Abstract

Equations are derived from the Navier-Stokes and energy equations for the correlations between velocities and temperatures at two points in a homogeneous turbulent field. Although uniform mean velocity and temperature gradients are present, in the field, the turbulence decays with time. Solutions are obtained by converting the equations to spectral form by taking their Fourier transforms and assuming that the turbulence is sufficiently weak for triple correlations to be negligible in comparison-with double correlations. Spectra of the turbulent heat transfer and of the mean square temperature fluctuation are calculated as a function of dimensionless velocity gradient. The ratio of eddy diffusivity for heat transfer to that for momentum transfer is also obtained. It is shown that the eddy diffusivity ratio approaches one at high velocity gradients regardless of the value of Prandtl number. However, its rate of approach to 1 is greatest for Prandtl numbers on the order of 1.