What is it about?
If you have a body sliding on a fluid, like a surfboard moving in a straight line, the viscosity of the fluid is responsible for the force exerted on the body. There exists a very thin layer close to the body where the effect of the viscosity is dominant. This is called "boundary layer". The description of the fluid velocity distribution in this layer is governed by the Blasius equation. Nowadays a simple solution to this equation was not yet found. Here we derive a strategy for obtaining an accurate approximation of this solution with a compact formula.
Featured Image
Photo by Gian Luca Pilia on Unsplash
Why is it important?
The solution of the Blasius equation is used in a wide class of problems spanning from thermal issues, such as the cooling of a flat plate due to an air stream over it (very frequent for electronic components), to turbulence, where the description of a turbulent layer over a flat plate is performed with an equation similar to Blasius one.
Perspectives
The use of this accurate and simple solution may stimulate a significant research in all the fluid dynamics area where the solution of Blasius equation is useful. For example, the passage from laminar to turbulent boundary layer is somewhat investigated still in a phenomenological manner, without a mathematical insight that may significantly improve the understanding of the physics behind it. This solution may help, by providing a simple formula with which test the disturbance propagation within a laminar stream.
Danilo Durante
Consiglio Nazionale delle Ricerche
Read the Original
This page is a summary of: An asymptotic matching approach to the approximate solution of the Blasius problem, Physics of Fluids, February 2023, American Institute of Physics,
DOI: 10.1063/5.0137563.
You can read the full text:
Contributors
The following have contributed to this page
