Radioactive wastes (krw 20 W/mK) are stored in a

QUESTION:

Radioactive wastes (krw 20 W/mK) are stored in a spherical, stainless steel (kss 15 W/mK) container of inner and outer radii equal to ri 0.5 m and ro 0.6 m. Heat is generated volumetrically within the wastes at a uniform rate of q . 105 W/m3 , and the outer surface of the container is exposed to a water flow for which h 1000 W/m2 K and T 25 C. (a) Evaluate the steady-state outer surface temperature, Ts,o. (b) Evaluate the steady-state inner surface temperature, Ts,i . (c) Obtain an expression for the temperature distribution, T(r), in the radioactive wastes. Express your result in terms of ri , Ts,i , krw, and q . . Evaluate the temperature at r 0. (d) A proposed extension of the foregoing design involves storing waste materials having the same thermal conductivity but twice the heat generation (q . 2 105 W/m3 ) in a stainless steel container of equivalent inner radius (ri 0.5 m). Safety considerations dictate that the maximum system temperature not exceed 475 C and that the container wall thickness be no less than t 0.04 m and preferably at or close to the original design (t 0.1 m). Assess the effect of varying the outside convection coefficient to a maximum achievable value of h 5000 W/m2 K (by increasing the water velocity) and the container wall thickness. Is the proposed extension feasible? If so, recommend suitable operating and design conditions for h and t, respectively.