Radioactive waste (k = 20 W/m · K) is stored in a cylindrical stainless steel (k = 15W/m · K) container with inner and outer diameters of 1.0 and 1.2 m, respectively. Thermal energy is generated uniformly within the waste material at a volumetric rate of 2 × 10⁵ W/m³. The outer container surface is exposed to water at 25°C, with a surface coefficient of 1000 W/m² · K. The ends of the cylindrical assembly are insulated so that all heat transfer occurs in the radial direction. For this situation determine
a. The steady-state temperatures at the inner and outer surfaces of the stainless steel
b. The steady-state temperature at the center of the waste material