The Effective Fuel Temperature to be Used for Calculating Resonance Absorption in a ²³⁸UO₂ Lump with a Nonuniform Temperature Profile

Calculations of resonance absorption for simple temperature profiles both in a slab and in a pin of ²³⁸UO₂ are presented to show the influence of a nonuniform fuel temperature profile on the choice of the equivalent uniform temperature, or the effective fuel temperature. The effective fuel temperature is given as a weighted average of the temperatures in the fuel zones. Two simple theoretical expressions for this weighted average, derived from the literature, are discussed. First, for high absorption, the effective fuel temperature is given by the so-called chord-averaged fuel temperature. Second, for low absorption, the effective fuel temperature is given by the volume-averaged fuel temperature. The results for a slab of ²³⁸UO₂ show that a bruteforce method is necessary to calculate an accurate effective fuel temperature. A set of weights for one specific ²³⁸UO₂ pin is calculated. This set agrees well with the chord-averaged fuel temperature. However, this appears to be a coincidence because the results for specific neutron energy ranges do not agree with this set of weights.