An improved model to predict the heat dispersion from an elevated line source in a turbulent boundary layer is presented in consideration of temperature structure. Three development stages of heat dispersion behind a line source are discussed. Especially the initial stage in the region which is close to the source is hardly represented by the simple gradient-diffusion model. In this study an effective turbulent Prandtl number is introduced to describe the nonequilibrium turbulent temperature field near the source. At the initial stage, the meandering motion of a thin thermal plume dominates mean temperature and turbulent heat flux. The effective turbulent Prandtl number contains the effect that the meandering motion increases as fluid flows downstream. The developing process of the turbulent temperature field is characterized by the temporal integral Lagrangian scale at the source location. Therefore modeling of the effective turbulent Prandtl number also needs the Lagrangian information. The effective turbulent Prandtl number is used in energy equation and the turbulent eddy viscosity is estimated by using the low Reynolds number model. κ-ε model The model predictions are compared with experimental results. The predictions of a two-equation model for heat transport are also included for comparison. The comparison shows that the present model performance is in better agreement with experimental data than the latter method. In addition the model computation reveals that the maximum temperature decays with a power law, $Θ_{max}~Δx^{-1}$ in the intial stage and $Θ_{max}~Δx^{-0.7}$ in the final asymptotic stage.
