A mathematical description of the fluid boundary layer

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...

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Bibliographic Details
Published in:Applied mathematics and computation 2006-04, Vol.175 (2), p.1675-1684
Main Author: Weyburne, David W.
Format: Article
Language:English
Subjects:
Boundary layer thickness
Computational methods in fluid dynamics
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematics
Partial differential equations
Physics
Sciences and techniques of general use
Thermal boundary layer
Velocity boundary layer
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2005.09.012