In this paper, the formation of the avalanche, primary streamer, secondary streamer, neutral gas heating effects, striations, as well as the radial expansion of the discharge from the symmetry axis toward the boundaries in a constant voltage atmospheric pressure air-dielectric barrier discharge configuration are analyzed. A voltage of 11.2 kV is applied between two metallic parallel plates which are placed at a distance of 4 mm apart. Two rectangular blocks of dielectric medium of 1 mm thickness, each with a relative permittivity of 8, are attached to the cathode and anode metallic electrodes, leaving the remaining 2-mm air gap for the atmospheric air discharge to develop. A single electron is released at the cathode as an initial condition and the development of the barrier discharge with its associated heating effects is analyzed. It has been shown that the discharge exhibits phenomena of radial expansion toward the outer boundaries, forming patterns of striations/filaments along the discharge and temperature rising of ambient air to 490 °K amounting to 63% increase above the ambient temperature. A secondary streamer has been observed traveling from the anode toward the cathode, after the primary streamer hits the cathode, and the primary and secondary streamer speeds were found to exhibit similar propagation speeds within the range 0.5 × 105 - 5 × 105 ms-1. The secondary streamer was found to be associated with electron charge densities of the order of 0.5 × 1018 - 1.5 × 1018 m-3, net charge densities of 1 × 1018 m-3 and radial and axial electric fields of 0.5 × 106 Vm-1.