A mixed-oxide (MOX) fuel rod in a small pressurised-water test loop runs at a linear…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Nuclear Physics · Temperature, heat and the macroscopic behaviour of matter

Energy from Physics, Ch Running a reactor: kinetics, heat removal, feedback, burn-up and the fuel cycle

Problem

A mixed-oxide (MOX) fuel rod in a small pressurised-water test loop runs at a linear heat rate of q′=22 kW m−1q' = 22\,\mathrm{kW\,m^{-1}}. Over the temperature range of interest its pellets have an effective thermal conductivity kth=2.8 W m−1 K−1k_{\rm th} = 2.8\,\mathrm{W\,m^{-1}\,K^{-1}}, taken as constant. Steady conduction with a uniform volumetric heat source in the cylindrical pellet gives 1rddr(rdTdr)=−q′′′/kth\dfrac{1}{r}\dfrac{d}{dr}\left(r\dfrac{dT}{dr}\right) = -q'''/k_{\rm th}. ((a)) Find the temperature rise from the pellet surface to its centreline. ((b)) State whether the pellet's radius was needed for this result, and why.

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