Problem 8 Thursday February 10, 2022 Radioactive wastes (kw = 25 Wm-K-) are to be stored in spherical stainless steel (ks = 18 Wm 'K-4) containers. The wastes generate thermal energy non-uniformly according to Qv = Q. 20[1- (+-)] [" where Q. = 175 kWm is the maximum rate of generation, r is the radial distance from the center of the container, and r; is the inner radius of the container. The outer surface of the container is cooled by 25C water with a convective heat transfer coefficient of h=1.0 kWm-K?. a. Safety considerations require that the maximum steady-state temperature of the system remain below 475C. Will a spherical container with inner and outer diameters of 1.0 m and 1.2 m, respectively, satisfy this requirement? b. Determine the steady-state temperature at the outer surface of the container in part (a). c. (Extra credit) If the solid wastes generated thermal energy uniformly, what would the maximum temperature be for the same total rate of energy generation within the container? d. It is proposed to use a spherical container of 1.0 m inner diameter for storing radioactive waste with the same thermal conductivity but twice the volumetric heat generation rate. Safety considerations require that the container wall thickness be no less than 3.0 cm. If the outside heat transfer coefficient can be increased up to a maximum value of 5.0 kWm-K-?, determine if the proposed design is feasible. If so, use plots of center temperature vs heat transfer coefficient to recommend operating and design conditions for h and container wall thickness