The scope of the study is restricted to solving these problems. The problems mainly include two-dimensional, unsteady, incompressible laminar boundary layer flows of electrically conducting Newtonian fluids in the vertical direction. The first problem mainly focus on free convection flow of Newtonian electrically conducting fluid in presence of chemical reaction and variable suction in`other hand, the third and fifth problems mainly focus on unsteady free convection flow of an electrically conducting Newtonian fluid in a vertical diction considering Dufour and Soret effects through a porous...