This study focuses on exploring innovative methods of energy conservation specifically through the nonlinear fin equation. To improve the heat transfer efficiency in cooling systems, the research suggests utilizing nano lubricants that possess superior thermo-physical properties. Unlike other nanofluids, the use of nanolubricants can decrease corrosion and abrasion in operational parts such as the bore-piston, gasket, and valve mechanisms. The study concentrates on the temperature distribution in both rectangular and longitudinal dovetail fins utilized in double-pipe heat exchanger applications. The energy equation is formulated to consider radiation, temperature-dependent internal heat generation, and wetted conditions, and is subsequently transformed into a dimensionless form. Numerical solutions to the resulting differential equation are obtained through the utilization of the collocation method. The study explores the use of a specific heat transfer liquid (ZnO-SAE 50) nanolubricant to analyze thermal dispersion in both straight rectangular and dovetail fins. Additionally, it investigates how temperature-dependent internal heat generation impacts convection-conduction heat transfer. The study finds that an increase in surface emissivity results in greater heat transfer through the fin's surface in the presence of nanolubricant.