Finite Element Solution of Temperature Distribution in a Circular Fin

The aim of this study is to analyze the temperature distribution in a circular fin with finite element method. We consider a annulus fin and heat transfers from the inner diameter outward to the outer diameter through the surface of the annulus. In this paper, the domain is divided into ten elements then the solutions of the equation are approximated by FEM in every nodes and according to the heat transfer equation and boundary conditions, we also obtain the related functional, the stiffness and the total force matrix. All calculations are done with Matlab then the results are compared with the exact solutions and also with the simulated solutions .It is noteworthy that Abaqus software is used for simulation and to obtain the exact solution, Bessel equation is used. The numerical results confirm that our method is of high accuracy and good convergence.

Keywords:

Circular Fin , Functional , Stiffness Matrix , FEM