(Solved): Thanks PROBLEM \# 2[ thermal energy generation in a spherical domain (25pts)] A 5cm diameter ...

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PROBLEM \# $$2[$$ thermal energy generation in a spherical domain $$(25\mathrm{pts})]$$ A $$5\mathrm{cm}$$ diameter radioactive sphere at steady state generates a total of $$40\mathrm{W}$$ of thermal energy. The sphere is covered by a layer of insulation $$27.5\mathrm{cm}$$ thick so that the total outside diameter is $$60\mathrm{cm}$$ The thermal conductivity of the radioactive material is $$4.0\mathrm{W}/(\mathrm{m}?\mathrm{K})$$. The thermal conductivity of the insulation is $$0.5$$ $$\mathrm{W}/(\mathrm{m}?\mathrm{K})$$. The insulated sphere is surrounded by a gas at $$25{}^{?}\mathrm{C}$$ with a convective heat transfer coefficient of $$20\mathrm{W}/\left({\mathrm{m}}^2\mathrm{K}\right)$$. Compute the temperatures at the following points: (a) Outside insulation surface. (b) Interface between radioactive material and insulation. (c) Centre of radioactive sphere The volume of a sphere is $$V=\frac{4}{3}?r^3$$ and the surface area of a sphere is $$A=4?r^2$$.