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Steady Plane Orthogonal Electromagneto-Fluiddynamic Incompressible Flows with Isometric Geometry

This work achieves two objectives in the study of steady plane orthogonal electromagneto-fluid dynamic incompressible flows when the charge density is not identically zero. The first objective was to give a method of solving flow problems and the second was to determine all possible flow geometries when the streamlines and their orthogonal trajectories form an isometric net. Integrability conditions are derived for two of the scalar fields and a method of solving flow problems is given along with two flow problems as our examples. Flows with isometric geometry are then investigated and the results obtained are our extension from ordinary fluid dynamics to these flows.