Radioactive waste is stored in a cylindrical stainless steel container with inner and outer diameters of 1 m and 1.2 m, respectively, so that R₀ = 0.5 m and R₁ = 0.6 m. 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 (T_∞ = 25°C), and the outer surface convective heat-transfer coefficient is h = 1000 W/m² · K. The ends of the cylinder are insulated so that heat transfer is only in the r-direction. You may assume that over the temperature range of interest the thermal conductivity of stainless steel, k_steel, is 15 W/m · K and the thermal conductivity of the radioactive waste, k_rw, is 20 W/m · K. 

a. What are the temperatures of the outer surface, T₀, and inner surface, T_i, of the stainless-steel container?

b. What the maximum temperature within the radioactive waste?

c. Where will this maximum temperature be located?