申論題

Problem 4 (25 pointsL Consider a spherical nuclear fuel element as shown in the following figure. It consists of a sphere of fissionable material with radius Rp, surrounded by a spherical shell of alumina cladding with outer radius of Rc. The thermal conductivity of the fissionable material is kp and that of the alumina cladding is kc. Inside the fuel element, the fissionable material generates heat with a rate per unit volume Sn, which is constant. Outside the element, heat is lost to the ambient environment with a constant temperature Ta and the heat flux can be described by the Newton's law of cooling with a heat transfer coefficient h. The heat transfer process has reached the steady state and the temperature in the element is a function of r (the radial coordinate) only.