The understanding of the radial distribution of temperature in a fuel pellet, under normal operation and accident conditions, is important for a safe operation of a nuclear reactor. Therefore, in this study, we have solved the steady-state heat conduction equation, to analyze the temperature profiles of a 12 mm diameter cylindrical dispersed nuclear fuels of U3O8-Al, U3Si2-Al, and UN-Al operating at 597 °C. Moreover, we have also derived the thermal conductivity correlations as a function of temperature for U3Si2, uranium mononitride (UN), and Al. To evaluate the thermal conductivity correlations of U3Si2, UN, and Al, we have used density functional theory (DFT) as incorporated in the Quantum ESPRESSO (QE) along with other codes such as Phonopy, ShengBTE, EPW (electron-phonon coupling adopting Wannier functions), and BoltzTraP (Boltzmann transport properties). However, for U3O8, we utilized the thermal conductivity correlation proposed by Pillai et al. Furthermore, the effective thermal conductivity of dispersed fuels with 5, 10, 15, 30, and 50 vol %, respectively of dispersed fuel particle densities over the temperature range of 27–627 °C was evaluated by Bruggman model. Additionally, the temperature profiles and temperature gradient profiles of the dispersed fuels were evaluated by solving the steady-state heat conduction equation by using Maple code. This study not only predicts a reduction in the centerline temperature and temperature gradient in dispersed fuels but also reveals the maximum concentration of fissile material (U3O8, U3Si2, and UN) that can be incorporated in the Al matrix without the centerline melting. Furthermore, these predictions enable the experimental scientists in selecting an appropriate dispersion fuel with a lower risk of fuel melting and fuel cracking.
New Galerkin-vector theory and efficient numerical method for analyzing steady-state heat conduction in inhomogeneous bodies subjected to a surface heat flux
