Question

list the assumptions (if appropriate), provide a sketch (if appropriate)

A spherical nuclear fuel pellet consists of a uranium core (thermal conductivity ku) of radius R with uniform internal energy generation q, surrounded by a layer of protective cladding (thermal conductivity ke) that does not have internal energy generation but has a thickness of t. The pellet is immersed in a large fluid bath with a temperature To and convection coefficient h. (a) Starting from the heat diffusion equation in spherical coordinates, determine the temperature as a function of radius (i.e., T(r)) in the uranium core, and put in terms of the known quantities given above. Hint: you will need two separate equations for the uranium and cladding, which are linked by the interface temperature they share. (b) If R=10 mm, t=1 mm, q=5x106 w/m2, Too-60°C, ku-10W/m-K, kc= 1.2 w/m-K, and h=400 w/m- K, what is the maximum temperature of the fuel pellet? Where does it occur in the pellet?

Answer 1

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