Consider a spherical nuclear fuel element as shown on the right. It consists of a sphere of fissionable material with radius RF, surrounded by a spherical shell of aluminum "cladding" with outer radius Rc. Inside the fuel element, fission fragments are produced that have very high kinetic energies. Collisions between these fragments and the atoms of the fissionable material provide the major source of thermal energy in the reactor. Such a volume source of thermal energy resulting from nuclear fission we call Sn ([=] energy/volume time). This source will not be uniform throughout . Coolant Aluminum cladding Sphere of fissionable TF(r) To RF material the sphere of fissionable material; it will be smallest at the center of the sphere, which can be approximated as follows: S₁ = SO [1+b(7)³] Where, Sno is the volume rate of heat production at the center of the sphere, b is a dimensionless positive constant, and r is the radial distance from the center of the sphere. The known temperature at the outside cladding surface (at r = Rc) is To. The thermal conductivities of the fuel element and cladding are kF and kc. Determine the temperature profiles in the fuel element and the cladding. Assume heat transfer occurs only in the r-direction.