Efficient formulation of the finite element method for heat conduction in solids

The purpose of the paper is to describe efficient methods and computer programs for analysis of heat conduction problems related to design and control of components of nuclear power plants and similar structures where thermal problems are of interest. A short presentation of basic equations and the finite element formulation of three-dimensional stationary and transient heat conduction is given. The finite element types that are used are isoparametric hexahedrons with eight or twenty nodes. The use of consistent as well as diagonal capacity matrices is discussed. Reduction of the transient heat conduction problem may be accomplished by means of the 'master-slave' technique. Furthermore, the superelement technique is discussed for both stationary and transient heat conduction. For the solution of transient problems, the trapezoidal time integration scheme is used. The methods and principles outlined in the paper are materialized in a computer program NV615, which is one of the application programs in the program system SESAM-69. A brief description is given of NV615.Furthermore, attention is given to combined heat conduction and subsequent thermal stress analysis. In order to investigate the accuracy and the efficiency of the methods, some heat conduction problems for which analytical solutions are known are analysed- specificilly: a) Semi-infinite solid with specified surface temperature, varying periodically with time. b) Semi-infinite solid with line heat source. Transient analysis. As an example of practical application the temperature distribution versus time in a turbine wheel during start up is analysed. Thermal stresses are calculated at selected time instants. (Auth.)