Fins are utilized to considerably increase the surface area available for heat emission between a heat source and the surrounding fluid. In this study, radial annular fins are considered to investigate the rate of heat emission from the surface to the surroundings. The effects of a ternary nanofluid, magnetic field, permeable medium and thermal radiation are considered to formulate the nonlinear ordinary differential equation. The differential transformation method, one of the most efficient approaches, has been used to arrive at the analytical answer. Graphical analysis has been performed to show how nondimensional characteristics dominate the thermal gradient of the fin. The thickness and inner radius of a fin are crucial factors that impact the heat transmission rate. Based on the analysis, it can be concluded that a cost-effective annular rectangular fin can be achieved by maintaining a thickness of 0.1 cm and an inner radius of 0.2 cm.