This book presents and discusses current research in the study of magnetohydrodynamics. Topics discussed include MHD free convection in a porous medium bounded by a vertical wavy wall and a parallel flat wall; the immersed boundary method; transient hydromagnetic natural convection between two vertical walls heated/cooled asymmetrically; the effect of suction/injection on MHD flat plate thermometer and flute and ballooning modes in the inner magnetosphere of the earth