This study develops a reliable finite-volume model, implemented in Python, to analyze nonlinear convective–radiative heat transfer in straight fins with nonuniform cross-sections and temperature-dependent properties, which are important in heat exchangers. The one-dimensional
steady-state nonlinear equations are solved using Python’s fsolve function. Model validation is first performed by comparison with exact solutions in the linear case and, unlike previous studies, is further benchmarked against a three-dimensional solver implemented in the open-source
OpenFOAM platform for the nonlinear case, demonstrating excellent agreement in both linear and nonlinear problems. Subsequently, the validated model is applied to investigate the temperature distribution and efficiency of triangular and rectangular fins under varying dimensionless
parameters. Results show that ambient fluid temperature affects fin efficiency in contrasting ways depending on whether the thermal conductivity parameter β is positive or negative. Within the investigated ambient temperature range, increasing the dimensionless temperature
of the ambient fluid can increase fin efficiency by up to 25% when β < 0, decrease it by up to 9% when β > 0, and remain nearly unchanged when β = 0. Overall, the model provides a valuable framework for investigating nonlinear heat transfer in fins, offering insights into their thermal
performance under varying conditions and supporting fin optimization.