Three-dimensional spatial direct numerical simulation is used to investigate the evolution of reactive plumes established on non-circular sources. Simulations are performed for three cases: a rectangular plume with an aspect ratio of 2:1, a square plume, and the square plume in a corner configuration. Buoyancy-induced large scale vortical structures evolve spatially in the flow field. A stronger tendency of transition to turbulence is observed for the free rectangular plume than the free square case due to the aspect ratio effect. Dynamics of the corner square plume differs significantly from the corresponding free case due to the enhanced mixing by the side-wall effects. A turbulent inertial subrange has been observed for the free rectangular and corner square plumes. Mean flow properties are also calculated. The study shows significant effects of source geometry and side-wall boundary on the flow transition and entrainment of reactive plumes.