Radioactive wastes are packed in a thin-walled spherical container. The wastes generate thermal energy non-uniformly according to the relation q = qo[1 – (r/r0)2], where q is the local rate of energy generation per unit volume, qo is a constant, and ro is the radius of the container. Steady-state conditions are maintained by submerging the container in a liquid that is at Too and provides a uniform convection coefficient h.

Determine the temperature distribution, T(r), in the container. Express your result in terms of q"0, r0, T∞, h, and the thermal conductivity k of the radioactive wastes.

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