O'Reilly Boisen1*, Rodrigues Nogueira2, Castillo Wankat3

ABSTRACT

Fins are engineered extended surfaces that significantly improve heat dissipation from a solid base to its surrounding environment. This work presents the design and thermal analysis of a parabolic-shaped fin, focusing on the distribution of temperature along its length under steady-state conditions. The heat transfer within the fin is modeled by solving nonlinear differential equations using the Shooting method, allowing accurate prediction of temperature profiles. Comparative evaluation is performed against a conventional rectangular fin of equal volume to quantify improvements in thermal performance. Both conduction within the fin and convection at its surface are incorporated into the analysis, leading to the derivation of fin efficiency and effectiveness equations. Results demonstrate that the parabolic fin achieves higher efficiency and superior heat transfer performance compared to the rectangular design. One-dimensional steady-state temperature profiles along the fin are plotted, providing insight into thermal gradients along the length. The system is mathematically modeled and simulated using MATLAB, illustrating the effectiveness of computational techniques in optimizing fin geometry and predicting heat transfer behavior in practical applications. Keywords: Extended surface; Parabolic fin; Thermal performance; Heat dissipation; Steady-state temperature; MATLAB simulation; Conduction and convection analysis; Fin optimization.