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The mathematical model describing the different aspects of physical problems as well as numerical method adopted for their solution have been introduced and discussed. The different phases of overall numerical solution procedure from their non-dimensional form through the similarity transformation to the solution of flow equations have been described. The boundary layer flow around bodies of different shapes like shrinking sheet, cylinder, inclined plate, moving surface, moving vertical plate, cone immersed in the fluid have been studied. These mathematical models are commonly encountered in many studies in aerodynamic, chemical engineering, hydrodynamic, wind engineering and ocean engineering etc. The study of various effects like chemical reaction, viscous dissipation, magnetic effect, thermal radiation etc. have been made to study their effects on velocity, temperature and concentration. The quantities of physical interest viz. skin friction, Nusselt number and Sherwood numberhave also been calculated and their analysis included in the study.