On magnetohydrodynamic flow over solids

• Main Author: Gourdine, Meredith Charles
• Format: Others
• Published: 1960
• Online Access: https://thesis.library.caltech.edu/5017/1/Gourdine_mc_1960.pdf; Gourdine, Meredith Charles (1960) On magnetohydrodynamic flow over solids. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5AMT-CM66. https://resolver.caltech.edu/CaltechETD:etd-12162005-083621 <https://resolver.caltech.edu/CaltechETD:etd-12162005-083621>

The steady flow of a viscous, incompressible and electrically conducting fluid over a solid, in the presence of an applied magnetic field parallel to the main flow, is considered. The equations of magnetohydrodynamics (MHD) are linearized by assuming that the solid only slightly perturbs the velocity and magnetic field. Fundamental solutions of the linearized equations are derived, and they are used to construct MHD flows over solids. The MHD drag formulas for the finite flat plate and the sphere are derived. The special cases of zero viscosity and infinite conductivity are studied, and general formulas for MHD forces on a solid are presented. The problem is generalized to include an electrical generator in the body. Steady flow over a flat, circular, broadside-on disk in the presence of a parallel magnetic field is solved as a boundary value problem. The flow solution and drag formulas are valid for all values of the three parameters, Reynolds number, Magnetic Reynolds number, and Alfven number. The drag is calculated for large and small magnetic interaction; in the latter case the drag is proportional to the Alfven number. A special diffusion model applicable for large Hartmann number flows is also presented.