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

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Abstract

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.

Original languageEnglish
Pages (from-to)235-239
Number of pages5
JournalJournal of the Physical Society of Japan
Volume27
Issue number1
DOIs
StatePublished - 1 Jan 1969
Externally publishedYes

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