An Implementation of the Finite Differences Method for the Two-Dimensional Rectangular Cooling Fin Problem

Abstract

The transport or advection-diffusion-reaction equation is a well-known partial differential equation employed to model several types of flux problems. The cooling fin problem is a particular case of such an equation. This work presents a straightforward model for the rectangular cooling fin in a problem. The model was based on the finite differences numerical method and an efficient implementation was developed in a high-level mathematical programming language. The accuracy was evaluated with different granularity levels of meshes, and two distinct boundary conditions are compared. In the first one, only prescribed temperatures are assumed at the four tips of the domain. For the second scenario, it is assumed a heat flux at one tip of a fin with the same geometrical shape. The achieved solutions produced by the algorithm were able to depict the temperature along the whole fin surface accurately. Furthermore, the algorithm reaches relevant performance for meshes up to 4257 points where the CPU time was about 33 seconds.