The study of convective heat transfer in differently shaped fins with radiation, internal heat generation and variable thermal conductivity was considered. The energy equation of the model was converted into the dimensionless form by adopting the proper variables, which was later solved using the differential transformation method. The impact of the parameters on the thermal performance, efficiency and heat transfer of the fins was analyzed graphically and also by performing thermal analysis on the fins. It was noticed that there was a significant effect on the thermal performance of the fins with different shapes, and also the heat transfer rate of the fin increased for improved values of the internal heat generation and radiation parameters. The exponential profile showed better results than other profiles, and the results obtained were supported by thermal analysis using ANSYS software.

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.