A Non-Linear, Finite Element, Heat Conduction Code to Calculate Temperatures in Solids of Arbitrary Geometry: The FEAT Program

Abstract

Structures often operate at elevated temperatures. Temperature calculations are needed so that the design can accommodate thermally induced stresses and material changes.

A finite element computer program called FEAT has been developed to calculate temperatures in solids of arbitrary shapes. FEAT solves the classical equation for steady state conduction of heat. The solution is obtained for two-dimensional (plane or axisymmetric) or for three-dimensional problems. Gap elements are used to simulate interfaces between neighbouring surfaces.

The code can model: conduction; internal generation of heat; prescribed convection to a heat sink; 'prescribed temperatures at boundaries; prescribed heat fluxes on some surfaces; and temperature-dependence of material properties like thermal conductivity. The user has an option of specifying the detailed variation of thermal conductivity with temperature. For convenience to the nuclear fuel industry, the user can also opt for pre-coded values of thermal conductivity, which are obtained from the MATPRO data base (sponsored by the U.S. Nuclear Regulatory Commission).

The finite element method makes FEAT versatile, and enables it to accurately accommodate complex geometries. The optional link to MATPRO makes it convenient for the nuclear fuel industry to use FEAT, without loss of generality. Special numerical techniques make the code inexpensive to run, for the type of material non-linearities of ten encountered in the analysis of nuclear fuel. The code, however, is general, and can be used for other components of the reactor, or even for non-nuclear systems.

The predictions of FEAT have been compared against several analytical solutions. The agreement is usually better than 5%. Thermocouple measurements show that FEAT predictions are consistent with measured changes in temperatures in simulated pressure tubes. FEAT was also found to predict well, the axial variations in temperatures in the end-pellets (UO₂) of two fuel elements irradiated in experimental and in commercial nuclear reactors.