Modeling of axisymmetric heat conduction in compact products of ceramic nuclear fuel with the temperature dependencies of thermophysical characteristics
Abstract
The possibilities of using of various mathematical formulations for modelling the axisymmetric heat conduction of compact products of ceramic nuclear fuel are discussed. It is shown that the application of the heat equation wrote with respect to temperature can introduce errors due to the uncertainty of the initial data on the derivative of the temperature dependence of the thermal conductivity, which is available exclusively in a tabulated form for temperature values separated by a sufficiently large step. This circumstance is essential for modelling the axisymme tric heat conduction of compact products of ceramic nuclear fuel, since its thermal conductivity depends significantly on temperature, decreasing by a factor of 2.5 with a temperature change from 323 K to 1073 K. It is shown that to study of the axisymmetric heat conduction of compact products of ceramic nuclear fuel, the most interesting is the mixed mathematical formulation of the heat conduction problem with respect to the temperature fields and the heat flux vector, since the corresponding differential equations do not contain the derivative of the temperature dependence of the thermal conductivity. In this case, the approximations of the values the thermal conductivity coefficient from the available tabular data will be limited by the error in approximating the values of the thermal conductivity, which is easily monitored from the available tabular data on the values of the thermal conductivity coefficient. To solve the heat conduction problem, formulated in mixed form with respect to the temperature fields and the heat flux vector, it is proposed to use the semi-discretisation method, which reduces the problem under consideration to determining the time dependences of the unknown quantities at individual points of the investigated region of a compact product of ceramic nuclear fuel. To this end, it is proposed to replace finite-difference formulas by finite-difference formulas only in terms of spatial coordinates, which will allow us to obtain ordinary differential equations with initial conditions for determining the nodal values of the unknown quantities.
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