In this book we analyze the basic concepts of fluids and unsteady MHD free convective boundary layer flows under varies initial and boundary conditions. The dimensionless governing equations are solved numerically using finite element method. The resultant expressions for velocity profiles, temperature profiles, concentration profiles, skin friction, rate of heat transfer and rate of mass transfer are calculated for various parameters occurring into the problem and are extensively discussed with the help of graphs and tables. I hope that this book will be useful for the students, researchers and teachers who are working on fluid dynamics and heat and mass transfer problems.