Magnetohydrodynamics (MHD) micropumps which have no moving parts have attracted attention from the microfluidics community. A significant amount of research is being reported in the design, fabrication and operation of such devices. In this work, we report analytical investigation of the physics of such devices and a development of a generalized numerical framework for the solution of the full 3D MHD equations that govern the multi-physics of MHD micropumps. Based on the numerical framework developed, we investigate different flow channel geometries influenced by the micromachining process, effects of non-uniform magnetic and electric fields, Joule heating, and electroosmosis in MHD micropumps.