LAMINAR HEAT TRANSFER FROM A FLAT PLATE WITH SMALL VELOCITY FLUCTUATION ON THE WALL
The distortion of the mean velocity distribution and the change in the mean heat transfer coefficient due to the small two and three dimensional velocity fluctuations of a single Fourier mode generated near a solid surface is investigated theoretically, for the laminar boundary layer flow over a flat plate using the Galerkin technique, when the amplitude of the fluctuation is small compared with the main flow velocity but the frequency and the wave number of the fluctuation are large. In the case of two dimensional velocity fluctuation, the Reynolds stress due to the velocity fluctuation decays in the thin Stokes layer and distorts the mean velocity profile, but its effect on the friction and the heat transfer rates of time mean is not very large. In the three dimensional case, the Reynolds stress is large throughout the boudary layer and the mean friction and heat transfer rates are much different from those without the fluctuation. In this case, the mean velocity profile can be expressed by a logarithmic form.