In this study, we continue with our previous renormalization group analysis
of incompressible turbulence, aiming at determination of various thermal t
ransport properties. In particular, the temperature field T is considered a
passive scalar. The quasinormal approximation is assumed for the statistic
al correlation between the velocity and temperature fields. A differential
argument leads to derivation of the turbulent Prandtl number Pr-t as a func
tion of the turbulent Peclet Pe(t) number, which in turn depends on the tur
bulent eddy viscosity nu (t). The functional relationship between Pr-t and
Pe(t) is comparable to that of Yakhot rt al. [Int. J. Heat Mass Transf. 30,
15 (1987)] and is in close consistency with direct-numerical-simulation re
sults as well as measured data from experiments. The study proceeds further
with limiting the operation of renormalization group analysis, yielding an
inhomogeneous ordinary differential equation for an invariant thermal eddy
diffusivity sigma. Simplicity of the equation renders itself a closed-form
solution of sigma as a function of the wave number k. which, when combined
with a modified Batchelor's energy spectrum for the passive temperature T,
facilitates determination of the Batchelor constant C-B and a parallel Sma
gorinsky model and the model constant C-p for thermal turbulent energy tran
sport.