Approximate Estimates of the Temperature State of Ceramic Nuclear Fuel in Cylindrical Fuel Elements and the Influence of Processes and Parameters of a Nuclear Reactor Core

Abstract

The approximate mathematical model of the temperature state of ceramic nuclear fuels in cylindrical fuel elements was proposed in the form of linear ordinary differential equation and the boundary conditions. The theory of heat conduction and assumptions about the axial symmetry and absence of heat flows along axis of fuel element, which allow to simplify the common equations in cylindrical coordinates, are the basis of the proposed simplified mathematical model for approximate estimating the temperature state of the nuclear fuel. The intensity of volume heat sources in fuel element was taken into account by using the average values corresponding with the heat power and the structural characteristics of a nuclear reactor core. The conception about the heat transfer coefficient was used for modeling interaction between the fuel and the heat carrier. This heat transfer coefficient depends on characteristic sizes and heat conductions of constituted materials of the fuel element and allows to estimate influence of these on the temperature state of the nuclear fuel. The analytical solution for the temperature of a ceramic fuel in cylindrical fuel elements was obtained and was used for researching. It was shown that the heat conductivity of the fuel has significantly influences both the average temperature and the difference between the inner and outer temperatures in the fuel pellet. At the same time, other parameters have significant influence only on the average temperature of the fuel pellet. Due to these, it is necessary to consider the temperature dependence of the thermal conductivities of the materials constituted the fuel elements for more precisely estimations the temperature state of the fuel pellets, which will lead to nonlinear equations will required the numerical methods for their solving.