The present paper was aimed to study the effects of variable thermal conductivity and heat generation on the flow of a viscous incompressible electrically conducting fluid in the presence of a uniform transverse magnetic field, thermal radiation, porous medium, mass transfer, and variable free stream near a stagnation point on a non-conducting stretching sheet. Equations of continuity, momentum, energy, and mass were transformed into ordinary differential equations and solved numerically using shooting method. Velocity, temperature, and concentration distributions were numerically discussed and presented in the graphs. Skin-friction coefficient, the Nusselt number, and Sherwood number on the sheet were derived and discussed numerically. Their numerical values for various values of physical parameters were presented in the tables. It was found that temperature increased with increasing radiation parameter, R, and concentration decreased with increasing the Schmidt number, Sc. The numerical predications were compared with the existing information in the literature and a good agreement was obtained.