In this work, heat conduction in a typical spherical fuel element (pebble) of a pebble-bed high temperature reactor was studied. The fuel element is composed by a particulate region with spherical inclusions, the UO2 fuel particles (TRISO), dispersed in a graphite matrix. The two energy equation model was applied to the particulate region, generating two macroscopic temperatures, respectively, of the fuel and of the matrix. Analytical solutions are obtained for steady-state heat conduction. Transient analysis was carried out by using the generalized integral transform technique (GITT), which requires low computational efforts and allows a fast evaluation of the two macroscopic transient temperatures of the particulate region. The solution by GITT leads to a system of ordinary differential equations with the unknown transformed potentials, which is solved numerically to obtain the hybrid solution of the original partial differential equation. Numerical results for several testing cases are presented.

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