Quasi-three-dimensional modeling of flow in MHD channels

A set of two-dimensional turbulent boundary-layer equations that describe the three-dimensional fluid flow in a magnetohydrodynamic channel is outlined. The equations are solved by an implicit finite-difference scheme; a method of calculating the pressure gradient is used that avoids the need to iterate over the coefficients of the difference equations. The numerical method is tested by applying it to lowand high-speed flows over a flat plate. It is shown that the governing equations fully satisfy the three-dimensional conservation laws. The importance of accounting for three-dimensional effects is assessed, and an advanced technique for bringing out better the interaction between the boundary layers on sidewalls and electrode walls is discussed.