The impact of Finite Elemen method for a Circular Fin

In this research we are going 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 essay, 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 ger 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 goodconvergence.

Keywords:

temperature distribution , Circular Fin , finite element method , Functional , Stiffness Matrix , exact solutions