Exact solutions of the unsteady hydrodynamic and hydromagnetic flows past an infinite plate (Q1113772)

Exact solutions for the hydrodynamic and hydromagnetic unsteady flows of an incompressible viscous fluid with general free stream velocity \([u_{\infty}=f(t)]\) are obtained. From the unsteady hydrodynamic solution, several existing solutions such as the steady-state solution of Meredith and Griffith for constant free stream velocity \((u_{\infty}=u_ 0)\) and the quasi-steady-state solution of \textit{J. T. Stuart} [Proc. R. Soc. Lond., Ser. A 231, 116-130 (1955; Zbl 0066.427)] for free stream oscillations \([u_{\infty}=u_ 0(1+\epsilon e^{i\omega t})]\) are obtained. Also, the solutions are found for finite and large values of t and for their asymptotic cases. These results are obtained for both hydrodynamic and hydromagnetic cases and are compared at each stage.