<p>Fins are extensively utilized in heat exchangers and various industrial applications as they are lightweight and can benefit in various systems, including electronic cooling devices and automotive components, owing to their adaptable design. Furthermore, spine fins are introduced to improve performance in applications such as automotive radiators. They can be shaped in different ways and constructed from a collection of materials. Inspired by this, the present model examines the effects of internal heat generation and radiation-convection on the thermal distribution in a wetted convex-shaped spine fin. Using dimensionless terms, the proposed fin model involving a governing nonlinear ordinary differential equation (ODE) is transformed into a dimensionless form. The study uses the operational matrix with the Charlier polynomial collocation method (OMCCM) to ensure precise and computationally efficient numerical solutions for the dimensionless equation. In order to aid in the analysis of thermal performance, the importance of major parameters on the temperature profile is graphically illustrated. The main outcome of the study reveals that as the radiation-conductive, wet, and convective-conductive parameters increase, the heat transfer rate progressively improves. Conversely, the ambient temperature and internal heat generation parameters show an inverse relationship.</p>