Solutions of the Magnetofluid-Dynamic Boundary-Layer Equations for a Flat Plate with a Moving Transverse Magnetic Field Source or Crossed Electric Field in the Spanwise Direction

摘要

The effects of a transverse magnetic field on velocity profiles in the boundary layer of a conducting fluid are investigated. A numerical technique is used to obtain solutions of the combination of continuity and momentum equations for flow of an incompressible fluid over a flat plate. Both variable conductivity and constant conductivity are studied. In the former case a magneticfield velocity ratio is defined and its effect on velocity profiles is examined. It is shown that when the magneticfield velocity ratio is zero, the magnetic effect will decrease skin friction; increase displacement thickness, momentum thickness, and net drag; and destabilize the boundary layer. These effects are reversed when the magnetic-field velocity ratio is greater than or equal to unity. Nonsimilarity effects are studied by solving the equations when the magnetic-interaction parameter is allowed to increase linearly with distance from the leading edge. The results show that for given values of the magnetic-interaction parameter and magnetic-field velocity ratio the effects are greater for a similarity solution than for a nonsimilarity solution; however, the similarity solutions are a fair approximation of the nonsimilarity except where the boundary layer is near separation, and here there is noticeable divergence.