Exact solutions of the unsteady hydrodynamic and hydromagnetic boundary layer equations in a rotating fluid system

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 nonresonant 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 nonresonant frequencies. It is shown that the ultimate steady-state flows are eventually established through inertial oscillations and the propagation of diffused waves. The nonexistence of the ultimate steady-state hydrodynamics 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.