This book investigates unsteady two-dimensional magneto hydrodynamic (MHD) free convective laminar boundary-layer flow problems in the presence of different physical parameters and subjected to different boundary conditions. The governing boundary layer partial differential equations have been solved by using the finite element method and the Laplace transform technique. Fluid-velocity, temperature, concentration, skin friction coefficient, Nusselt number and Sherwood number are calculated for various parameters occurring into the problem and are extensively discussed with the help of graphs and tables. It is hoped that this book will be useful for the students and researchers who are working on fluid dynamics and heat and mass transfer problems.