(1) A sphere of decaying radioactive material of radius r0 produces heat at a rate of q(W/m3). The sphere is contained in a spherical shell of graphite of outside radius r1. The outside surface of the graphite is cooled uniformly by flowing air of temperature T. The heat transfer coefficient at the outside surface is h. The constant thermal conductivities of the radioactive material and the graphite are k0 and k1, respectively. Densities and heat capacities are 0,c0 and 1,c1, respectively, following this subscript convention. The one-dimensional, transient heat equation with heat generation, for a region of constant k, in a spherical coordinate system, is r21r(r2rT)+kq=kctT (a) Write one-dimensional heat equations governing the radioactive material and governing the graphite shell, for steady-state conditions. (One heat equation for each region). (b) Define the boundary conditions required to solve for the steady-state temperature distribution throughout the composite