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Aeronautical Engineering analytic function approximate integral method approximate method body boundary conditions boundary-layer thickness characteristic length convergence coordinate CORNELL UNIVERSITY current sheet dimensionless velocity discussed electrical conductivity equation of viscous equations 1.1 equations 2.11 equations 2.27 exact solution field vector finite five unknowns flat plate flat-plate problem fluids with large Frcm free stream gives higher derivatives infinity integral equations integral momentum equation layer equations layer theory layer thickness Lewellen magnetic boundary layer magnetic Prandtl number MAGNETIC PROFILES magnetic-boundary negative non-dimensional ordinary differential equations outer flow parallel magnetic field PENNSYLVANIA STATE UNIVERSITY plot previously region satisfied School of Aeronautical seen separated profile shape parameter similar flow similar solutions singularity solution for oC solved stagnation flow stream and parallel sub-Alfvenic flow system of equations tody values of oC velocity and magnetic velocity component velocity profile viscous boundary layer viscous layer viscous theory wedge angle