Second-order Reynolds stress/heat flux closure models are applied to predict the turbulent thermal dispersion behind a line heat source in a uniformly sheared flow and behind a cylinder in a uniform velocity flow : closure models are investigated for $\overline{u_iu_j^θ}$ and $\overline{u_iθ^2}$ which appear in the second moment equations for the Reynolds stress $\overline{u_i u_j}$, scalar flux $\overline{u_iθ}$ and scalar variance $\overline{θ^2}$. The exact governing equations for Reynolds stress, heat flux and other scalar fluctuating quantities are formulated and modeled. The concept of effective buoyancy Reynolds stress
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is introduced to incorporate the buoyancy effect in the turbulent thermal diffusion. In addition, buoyancy effect
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is considered also in time scale in order to consider the suppression effect in stable area of turbulent flow. The model predictions are compared with the relevant experiments. The simple gradient transport model predictions are also included for comparison. The predictions for the proposed models were compared with the two experiments for the turbulent wake behind a line heat source and a cylinder in a uniformly sheared flow. For the weekly shear flow, the calculated results are acceptable although there is some discrepancy between calculation and measurement for the turbulent shear stress. It was found that the present model proposed in this study yields much better numerical values when applied to predict third-order transport terms in the vertical direction like $\overline{ν^2θ}$, $\overline{νθ^2}$ in comparison with the simple gradient model. For all the variables in a wake flow behind a cylinder experiment, the agreement between prediction and measurement is also very excellent. Therefore, the adopted second-order thermal turbulence model is capable of simulating the thermal dispersion in free wake flows. As compared with the simple gradient model, it was revealed that the present model predictions are in overall better agreement with the experiment. Furthermore, the buoyancy influence on the triple moments is significant in the present thermal dispersion problem behind a line heat source. However, the streamwise transports of second-order moments are slightly under-predicted as compared with the vertical transports of the same moments. It may be occurred from the fact only one velocity timescale has been used for the streamwise as well as the vertical turbulent transport predictions. The proposed model performance is shown to be generally satisfactory.
