Application of the Laplace Transform to the Solution of the Boundary Layer Equations. III. Magnetohydrodynamic Falkner-Skan Problem

The boundary layer equations for the magnetohydrodynamic version of the Falkner-Skan problem are solved with the use of the Laplace transform and the steepest descent technique. For the boundary layer flow of an electrically conducting fluid, past a semi-infinite flat plate, the viscous stress at the plate disappears when the adverse magnetodynamic pressure gradient is close to 1/11 U _∞²(1-S)x^-13/11. The quantity S gives the ratio of the magnetic to kinetic energy and U_∞ is the uniform velocity at the main flow. The possibility to extend the Laplace transform method to the evaluation of infinite integrals connected with the boundary condition at infinity is also demonstrated.