Problem $3$

Polymerization is an important process which is being carried out in a spherical reactor whose walls are well protected to maintain the inner temperature of $\backslash (300^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and the out temperature at $\backslash (30^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ with an overall outer diameter of $1000$ mm which is a composite of two materials. The inside wall is $100$ mm thick while the outer wall is $200$ mm thick. If the thermal conductivity of inner and outer walls are $5\mathrm{.}0$ and $\backslash (0\mathrm{.}5\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}\backslash$cdot $\backslash$mathrm$\{$K$\}\backslash ),$ respectively, Estimate the Rate of heat transfer through the reactor composite wall and Temperature at the junction of two walls.