Thermal plumes issued with mean exit velocities of 0.527 and 0.702 m/s from internally closed annular nozzles are investigated experimentally, theoretically, and numerically. The experimental setup and the measurement and analysis methodologies for flow and mixing are described in detail. The experimental setup consists of an air heating box with an annular slot of 0.12-m mean diameter and 0.01-m width, accompanied by equipment for setup operation and measurement of mean velocities and temperatures. The trajectory of maximum velocities and the isovelocity contours indicate reattachment due to plume self-merging at \(z_{\textrm{P0}}= 0.161\) m and around 0.20 m in correspondence to exit velocities. It was found that \(z_{\textrm{P0}}\) depends mainly upon initial Froude number and annulus equivalent diameter. Experiments detected a vortex ring right after the exit followed by a stagnation point at \(z_{\textrm{P1}}\cong 0.055\) m on the plume centreline. The annular plume core obtains almost uniform temperature and on average 15 times higher dilutions than bulk dilutions of the equivalnt round plume. To predict the self-merging trajectory, a novel integral model was developed named self-merging approach (SMA). SMA is based on the solution of the ordinary differential equations of momentum and buoyancy applied to an infinitesimal sector of the annular plume, which is equivalent to two identical slot plumes. These plumes are reattached due to outer entrainment, inner entrainment starvation, and a series of sinks along the annular plume centreline with strengths calculated by an original relationship. SMA predictions agree very well with the observations. The present findings contribute to a better understanding of the phenomenon and offer new ideas for designing buoyancy-operating disposal systems with low momentum, using annular- or rosette-type diffusers mainly in shallow water bodies.