Question: Consider a radioactive sphere, with outer radius r1, that is cooled with water in a container. Heat is generated uniformly in the sphere g (W/m3)

Consider a radioactive sphere, with outer radius r1, that is cooled with water in a container. Heat is generated uniformly in the sphere g (W/m3) due to to the characteristics of the radioactive material. The outer surface of the sphere dissipates heat to water that is at a temperature T with a coefficient combined convection h. Assuming steady state and conduction one-dimensional, determine: (a) Mathematical model (governing equation with boundary conditions). (b) Variation of the temperature in the sphere and the heat flux in the surface abroad. (c) Considering that r1=0.2m, , k =20 W/mC and g =45000 W/m3. Determine the temperature, in the center and the surface of the sphere, in addition to the heat flux in the outer surface" q(W/m2) at r2=0.2m. The convection coefficient is h=200 W/m2 C and the free flowing temperature of the water is T=20C.

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