A mathematical description of the fluid boundary layer

摘要

A method is developed for describing the fluid boundary layer formed adjacent to a solid due to fluid flow. The method is based on the observation that for laminar flow over a flat plate, the second derivatives of the velocity and temperature in the direction normal to the plate have a Gaussian-like profile. Borrowing from probability distribution function methodology, we describe the boundary layer in terms of the moments of these Gaussian-like kernels. The most important result is a physically meaningful measure of the boundary layer thickness. Several other new parameters are also developed which taken together allows one to describe the behavior of the velocity and temperature profiles in the boundary layer region in a much more comprehensive manner that is currently available. Laminar flow past a heated flat plate is used to demonstrate the method.