Premium
Stability of Poiseuille flow in an anisotropic porous layer with oblique principal axes: More accurate solution
Author(s) -
Shankar B.M.,
Shivakumara I.S.
Publication year - 2021
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/zamm.201900264
Subject(s) - streamlines, streaklines, and pathlines , anisotropy , principal axis theorem , isotropy , hagen–poiseuille equation , mechanics , transverse isotropy , porous medium , reynolds number , geometry , mathematical analysis , mathematics , flow (mathematics) , classical mechanics , materials science , physics , porosity , optics , turbulence , composite material
The stability of fluid flow in an anisotropic porous medium of Brinkman type is investigated. Anisotropy in the permeability is considered such that its longitudinal principal axis is oriented arbitrarily with the horizontal, while transversely it is isotropic. A fourth‐order eigenvalue problem obtained by performing a linear stability analysis is solved numerically using the Chebyshev collocation and the compound matrix methods. The critical Reynolds number and the critical wave number are computed for different values of porous parameter, orientation angle of the principal axis and the mechanical anisotropy parameter. The porous and the mechanical anisotropy parameters disclose contrasting contributions to the stability of fluid flow. The orientation angle instills either stabilizing or destabilizing effects on the fluid flow depending on the value of anisotropy parameter. Besides, the streamlines of the perturbation modes are presented for various values of orientation angle and anisotropy parameter. For the Darcy case, a simple analytical method is employed and established that the flow is stable for all infinitesimal perturbations.