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A nuclear fuel element consists of a solid cylindrical pin of radius, r1 and thermal conductivity,...

A nuclear fuel element consists of a solid cylindrical pin of radius, r1 and thermal conductivity, kf. The fuel pin is in good contact with a cladding material of radius, r2 and thermal conductivity, kc. Consider steady state condition for which uniform heat generation occurs within the fuel at a volumetric rate, g (w/m3 ) and the outer surface of the cladding is exposed to a coolant that is characterized by temperature, Tsur and convection coefficient, h.

a) Obtain equations for the temperature distribution Tf(r) and Tc(r) in the fuel and cladding, respectively.

b) Consider a uranium oxide fuel pin for which kf = 2 W/m.K and r1 = 6 mm and cladding for which kc = 25 W/m.K and r2 = 9 mm. If g = 2×108 W/m3 , h = 2000 W/m2 .K and Tsur = 300 K, what is the maximum temperature in the fuel element?

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