What is it about?
The authors obtained, for the first time, an exact analytical (by hand) solution to a long standing fluid mechanics problem posed in 1961 that previously required a numerical solution. The problem is that of a boundary layer along a moving wall, referred to as the "Sakiadis problem" .
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Why is it important?
The Sakiadis problem is important to the production of many products, including the printer paper that we use every day. The "analytical" solution provided can be viewed as a "special function" such as those represented by buttons on a calculator. The authors provide the short collection of formulas needed to implement the function. For convenience, a code is provided here: https://www.mathworks.com/matlabcentral/fileexchange/157956-sakiadis-function-exact-analytical-solution
Perspectives
Power series solutions to nonlinear ordinary differential equations (ODEs) is a topic dear to the authors. Although such solutions typically diverge well-within the physical domain of a problem (due to singularities not in the physical domain), all of the information to "analytically continue" the series beyond the divergence barrier is hidden within the series. For this problem, we were able to uncover that information and subsequently replace a collection of infinite terms with limited utility with a collection of infinite terms that convergences over the full physical domain. This gives us hope for similar problems and supports power series as a useful solution method for nonlinear ODEs.
Nathaniel Barlow
Rochester Institute of Technology
Read the Original
This page is a summary of: Exact and explicit analytical solution for the Sakiadis boundary layer, Physics of Fluids, March 2024, American Institute of Physics,
DOI: 10.1063/5.0199302.
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