A problem of a micropolar magnetohydrodynamic boundary- layer flow

The matrix exponential method, which constitutes the basis of the state space approach of modem control theory, is applied to the nondimensional equations of unsteady boundary layer flow past an infinite plane surface with a pressure gradient. Laplace-transform techniques are used. The results obtained can be used to generate solutions in the Laplacetransform domain to a broad class of problems in magneto-hydrodynamic boundary layer flow. The technique is applied to the problem of an electrically conducting micropolar fluid flowing past a vertical plane surface in the presence of a transverse magnetic field and to the problem of flow between two parallel plates. A numerical method is employed for the inversion of the Laplace-transforms. Numerical results are given and illustrated graphically for both problems.