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State Space Approach to Viscoelastic Fluid Flow of Hydromagnetic Fluctuating Boundary‐Layer through a Porous Medium
Author(s) -
Ezzat M. A.,
AbdElaal M. Z.
Publication year - 1997
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.19970770307
Subject(s) - laplace transform , viscoelasticity , mechanics , mathematical analysis , magnetic field , porous medium , boundary value problem , boundary layer , physics , classical mechanics , mathematics , porosity , materials science , thermodynamics , quantum mechanics , composite material
The method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, is applied to the non‐dimensional equations of a viscoelastic fluid flow of hydromagnetic fluctuating boundary‐layer through a porous medium bounded by an infinite non‐magnetic vertical plate. The formulation is valid for one‐dimensional problems. The resulting formulation together with the Laplace transform technique is applied to a variety of problems. The solution to a problem of an electrically conducting viscoelastic fluid in the presence of a transverse magnetic field and to a problem for the flow between two parallel fixed plates is obtained. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the velocity distribution and the induced magnetic field are given and illustrated graphically for each problem.