Magnetohydrodynamics (MHD) is emerged as academically new discipline before nine decade. In this book, we have discussed the steady/unsteady fully developed natural convective flow in different physical conditions under the presence of a magnetic field. First chapter is an introductory nature. Chapter II, IV and VI analyses the steady fully developed natural convective flow of an electrically conducting, viscous & incompressible fluid between two vertical walls or concentric annuli under constant/radial varying magnetic field. In chapter III, & V, we have discussed the momentum and heat transfer characteristics of unsteady magnetohydrodynamic natural convective flow of a viscous incompressible & electrically conducting fluid past over the semi-infinite vertical wall/channel.