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Calculate the thermal utilization factor for a heterogeneous lattice made up of cylindrical uranium rods of diameter 3cm and pitch 18cm in graphite Take the flux ratio φmU as 1.6 

Densities : Uranium = 18.7 × 103 kg m−3 , Graphite = 1.62 × 103 kg m−3 Absorption cross-sections σav = 7.68 b; σam = 4.5 × 10−3 b.

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The absorption rate in the fuel is 

ΣauφuVu 

where V is the volume, and the absorption rate in the moderator is 

ΣamφmV

The fraction of thermal neutrons absorbed by the Uranium fuel as compared to the total number of thermal neutron absorptions in the assembly is known as the thermal utilization factor f and is given by

Fig. 8.12 shows a unit cell of a heterogeneous assembly in which the uranium rods of radius r, are placed at regular intervals (pitch). The equivalent cell radius r1 is also indicated.

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