The aim of the present study is to extend air-cooling capabilities. A method of generating an unsteady vortical flow within small annular channels is introduced and studied numerically. The addition of an orifice at the entrance to the channel generates a propagating train of vortex rings that induces the continuous eruption of hot air from the wall region into the core flow. The overall effect is significant transverse convection even in laminar flows and enhancement of heat transfer. The effect of the orifice diameter is studied in detail. The method is very appealing for extending cooling capabilities of heat-sinks based on air, but it works similarly well for single phase flow of liquid. An increase of almost two-fold in the heat dissipation relative to a standard microchannel can be obtained. Heat dissipation of 8watt/cm2 per contact area can be anticipated using a single layer of the proposed air-based orificed-microchannel.