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ENTRY FLOW IN A CHANNEL
EXTENSION OF HUNTLE1B0VTCH SOLUTION TO LARGE
CHANNEL WITH A STEPANALYSIS
analysis Appendix approximation asymptotic expansion bluff bodies boundary conditions boundary layers boundary-layer expansion boundary-layer theory Chapter coefficients completing the contour core solution derived determined difference quotient differential equation downstream inside Dyke ENTRY FLOW equa equations 3-l expanded for large finite difference Fluid Mech Fourier transform full equations global circulation half-plane Hartmann layer inertial layer equations inertialess inlet inner expansion integration inviscid surface speed irrotational entry leading and trailing leading edge leading term linear Lorentz force lower half planes Ludford layer Magnetohydrodynamic matching MHD flow Navier-Stokes equations no-slip conditions nonlinear numerical obtain p=o r=o perturbation Poiseuille flow problem result Reynolds number satisfied second-order separation bubble shown in Figure similarity solution skin friction stagnant stagnation point stream function streamline strong transverse magnetic tion trailing edges transverse magnetic fields uniform entry upper half-plane upstream values vanishes velocity vertical viscous walls change slope Wiener-Hopf x-velocity yields