Transient one-dimensional heat conduction problems solved by finite element

Abstract

This paper establishes a solution method for the one-dimensional (1D) transient temperature and thermal stress fields in non-homogeneous materials. Finite-element method is used to space discretization, which results in a system of first-order differential equations. Transient solutions of these differential equations are obtained via either direct numerical difference or mode superposition. The formulation and system of equations are established in a very concise way. For 1D plates, axially symmetric cylinders and rotationally symmetric spheres, explicit expressions are given and the corresponding finite-element formulations are easily programmed. Moreover, stress analysis can be made from the calculated temperature field. Some sample examples are provided to show the applicability and effect of the proposed method.