Analysis of Effects of Free-Stream Turbulence on Heat Transfer and Skin Friction

A model for the momentum eddy diffusivity induced by free-stream turbulence was constructed on the basis of measured turbulent velocity fluctuations. The thermal eddy diffusivity was obtained via the turbulent Prandtl number. The general eddy diffusivity model was applied at the stagnation point of a cylinder situated in a uniform crossflow. The expression for the eddy diffusivity contains a single unknown constant which was determined from experimental stagnation point heat transfer results. Nusselt numbers and friction factors were evaluated from solutions of the governing conservation equations, and comparisons were made with available data and other predictions. The present analytical results agree well with the data and exhibit a behavior whereby, in concert with the data, the Nusselt number (and friction factor) increases with the free-stream turbulence intensity but to a lesser extent as the turbulence intensity increases. The effect of free-stream turbulence on the friction factor is shown to be substantially less than the effect on the Nusselt number.