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Note on Spectra from the Relaxed Boundary Conditions
Author(s) -
Chu Z.K.H.
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200103)81:3<211::aid-zamm211>3.0.co;2-g
Subject(s) - knudsen number , hagen–poiseuille equation , reynolds number , slip (aerodynamics) , boundary value problem , mechanics , spectral line , flow (mathematics) , physics , mathematics , mathematical analysis , thermodynamics , quantum mechanics , turbulence
A numerical investigation of the spectra of the Orr‐Sommerfeld equation for plane Poiseuille flow in macro‐ and micro‐channels is presented. The basic flow for the latter is modified by the slip‐flow effect given in terms of the Knudsen number. The numerical approach is a modified one (with complex matrix pre‐conditioning) of spectral methods. The relaxed results are compared with the non‐relaxed ones which are subjected to the no‐slip boundary conditions. This relaxed slip‐flow effect becomes the more dominant the more the size of the micro‐channel decreases because then the critical Reynolds number decreases.