High-Fidelity Calculation of Effective Thermal Response of Composite Media With Heat Generation Source

Abstract

The complexity of conductive heat transfer in a structure increases with heterogeneity (e.g., multi-component solid-phase systems with a source of internal thermal heat generation). Any discontinuity of material property — especially thermal conductivity — would warrant a thorough analysis to evaluate the thermal behavior of the system of interest. Heterogeneous thermal conditions are crucial to heat transfer in nuclear fuel assemblies, because the thermal behavior within the assemblies is governed significantly by the heterogeneous thermal conditions at both the system and component levels. A variety of materials have been used as nuclear fuels, the most conventional of which is uranium dioxide, UO2. UO2 has satisfactory chemical and irradiation tolerances in thermal reactors, whereas the low thermal conductivity of porous UO2 can prove challenging. Therefore, the feasibility of enhancing the thermal conductivity of oxide fuels by adding a high-conductivity secondary solid component is still an important ongoing topic of investigation. Undoubtedly, long-term, stable development of clean nuclear energy would depend on research and development of innovative reactor designs and fuel systems. Having a better understanding of the thermal response of the unit cell of a composite that represents a fuel matrix cell would help to develop the next generation of nuclear fuel and understand potential performance enhancements. The aim of this article is to provide an assessment of a high-fidelity computational model response of heterogeneous materials with heat generation in circular fillers. Two-dimensional, steady-state systems were defined with a circular, heat-generating filler centered in a unit-cell domain. A Fortran-based finite element method (FEM) code was used to solve the heat equation on an unstructured triangular mesh of the systems. This paper presents a study on the effects of a heat-generating filler material’s relative size and thermal conductivity on effective thermal conductance, Geff, within a heterogenous material. Code verification using the method of manufactured solution (MMS) was employed, showing a second-order accurate numerical implementation. Solution verification was performed using a global deviation grid convergence index (GCI) method to assess solution convergence and estimate solution numerical uncertainty, Unum. Trend results are presented, showing variable response in Geff to filler size and thermal conductivity.