(Solved): Consider a hollow pure copper sphere with inner and outer radii of 0.5 and 1m, respectively. The ...

Consider a hollow pure copper sphere with inner and outer radii of $$0.5$$ and $$1\mathrm{m}$$, respectively. There is an internal heat generation in the cylinder of $$5\times 10^5\mathrm{W}/{\mathrm{m}}^3$$. The temperature of the sphere at its inner and outer surfaces is of $$300^{?}\mathrm{C}$$ and $$600^{?}\mathrm{C}$$, respectively. (a) Departing from the Heat Diffusion Equation (HDE), do the problem formulation: state the simplified differential equation and BC's. (b)Departing from the problem formulation in part (a), obtain the temperature distribution inside the sphere, $$\mathrm{T}(\mathrm{r})$$. (c) Derive and obtain the maximum temperature in the sphere $$\left({}^{?}\mathrm{C}\right)$$ and its radial location