A $2$ cm $-$long cylindrical transistor with O$.$D$.0\mathrm{.}5$ mm should be electronically insulated by a material with thermal conductivity of $\backslash (0\mathrm{.}1\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}\backslash$cdot $\backslash$mathrm$\{$K$\}\backslash ).$ Assume that air temperature is $300$ K in its working environment with an associated convective heat transfer coefficient of $\backslash (20\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash$cdot $\backslash$mathrm$\{$~K$\}\backslash ).$ If the dissipated heat is $0\mathrm{.}2$ W $,$ determine $($a$)$ the radius of the insulation layer for the best cooling effect $(5\text{'})$ and $($b$)$ working temperature of the transistor with the optimal insulation design. $(5\text{'})$