Analysis of temperature distribution in a heat conducting fiber with convection losses using finite element method

Abstract

The temperature distribution in a heat conducting fiber is computed using the Galerkin Finite Element Method in the present study. The weak form of the governing differential equation is obtained and nodal temperatures for linear and quadratic interpolation functions for different mesh densities are calculated for Neumann boundary conditions. The results show that using a mesh of three quadratic elements produces a maximum error of 0.622 compared to 1.1832 for a similar number of linear elements. It is concluded that as the mesh is refined further progressively, the finite element solution approaches the exact solution admirably. The results are displayed in
both graphical and tabular forms