In the present paper, an attempt is made to discuss the heat and mass transfer effects on a laminar, two dimensional, steady/unsteady, free/mixed convection flow of an incompressible electrically conducting and radiating viscous fluid (or nanofluid) past a linear/non-linear stretching sheet / stretching cylinder bounded by a porous (or non-porous) medium, in the presence of various effects such as MHD, chemical reaction, viscous dissipation, thermophoresis, Brownian motion, thermally stratified medium, variable thermal conductivity and partial slip. This paper deals with the study case. The governing equations of the flow under consideration were solved with the associated boundary conditions by using a widely used numerical method called Runge-Kutta fourth order scheme along with shooting technique. In order to get a physical insight into the problems, the effects of various thermo-physical and hydrodynamical parameters on the velocity, temperature, concentration, skin-friction, Nusselt number and Sherwood number are computed and represented in figures and tables, and discussed in detail.