Radioactive wastes (krw = 20 W/m ∙ K) are stored in a spherical, stainless steel (kss, = 15 W/m ∙ K) 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 = 10-5 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' k rw , and q. Evaluate the temperature at r = O.

(d) A proposed extension of the foregoing design involves storing waste materials having the same thermal conductivity but twice the heat generation (q = 2 X 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 hand t, respectively.

Transcribed Image Text:

5 sin 24 = 273 + To, (K) 0<1<12h ) T, o(K) = 273 + 11 sin 24 12