Efficient Finite Element and Differential Quadrature Methods for Heat Distribution in One-Dimensional Insulated-Tip Rectangular Fin

Abstract

There are many numerical solution techniques acquainted by the computational mechanics community including the finite element method (FEM) and differential quadrature method (DQM). Usually elements are sub-divided uniformly in FEM (conventional FEM, CFEM) to obtain temperature distribution behavior in a fin. In CFEM extra computational complexity is needed to obtain a better solution with required accuracy. In this paper, non-uniform sub-elements techniques are considered for the FEM (efficient FEM, EFEM) solution to reduce the computational complexity. Then EFEM is applied for the solution of the one-dimensional heat transfer problem in an insulated-tip thin rectangular fin. The results are compared with CFEM and efficient DQM (EDQM, with non-uniform mesh generation). It is observed that EFEM exhibits more accurate results compared to CFEM and EDQM. The proposed techniques are showing the potentiality of the heat transfer related problem.