Direct numerical simulations of a turbulent plane Couette flow are combined with Lagrangian scalar tracking of thermal markers that are released in the flow field to determine the behavior of an instantaneous scalar line source located at the wall. The resulting probability density functions are used to calculate the behavior of instantaneous line sources of heat at the wall of the channel. The method is applied for fluids with a range of molecular Prandtl number, Pr, between 0.1 and 15,000, giving emphasis on the high Pr cases. The issues that are investigated are the effect of the Pr on turbulent dispersion, and the effect of the turbulence structure on turbulent heat transfer. The flow field for plane Couette flow is fundamentally different than that for channel flow, because the whole Couette flow domain is a constant stress region that forms an extensive logarithmic layer. For an instantaneous source at the wall, it is found that in both the channel flow and the Couette flow cases there are similar stages of development of the marker cloud that depend on the Prandtl number. This dependence becomes stronger as the Pr increases. However, this similarity is only qualitative.
