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Exact Solutions of the Unsteady Hydrodynamic and Hydromagnetic Boundary Layer Equations in a Rotating Fluid System
Author(s) -
Debnath L.
Publication year - 1975
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.19750550712
Subject(s) - mechanics , boundary layer , physics , steady state (chemistry) , laplace transform , suction , flow (mathematics) , classical mechanics , boundary value problem , blasius boundary layer , boundary layer thickness , mathematical analysis , thermodynamics , mathematics , chemistry , quantum mechanics
This paper provides a general study of the unsteady hydrodynamic and hydromagnetic boundary layer flows including the effects of the pressure gradient and uniform suction or blowing. Exact solutions of the boundary layer equations are obtained by using the Laplace transform treatment. Asymptotic analysis is carried out to determine the unsteady flow field for small and large times. The structure of the velocity distribution and the associated boundary layers is investigated for resonant and, non‐resonant cases with physical significance. The ultimate steady‐state hydrodynamic and hydromagnetic boundary layer flows are examined for various cases related to uniform suction or blowing, resonant and non‐resonant frequencies. It is shown that the ultimate steady‐state flows are eventually established through inertial oscillations and the propagation of diffused waves. The non‐existence of the ultimate steady‐state hydrodynamic solution for the case of resonance and blowing is investigated with physical significance. In the hydromagnetic situation, the ultimate boundary layer flow is found to exist for all cases involved in the problem including the case of blowing and resonance. Several special results of interest are discussed.