Problem $1($Conduction$)$

An aluminum nanoparticle is embedded in a polymer thin film. The Al particle has a diameter of

${10}^{-7}m,$ and the thin polymer film is ${10}^{-6}m$ thick. Beneath the polymer film is a ${10}^{-7}$ thick film of

silver. The particle absorbs from an external laser and heats the surrounding polymer. We want

to estimate the steady state temperature profile of the polymer film due to the particle heating. To

do this, we will estimate an effective thermal conductivity for the composite polymer$/$silver film

in the radial $\text{'}r\text{'}$ direction. Assume the bottom surface of the silver film is insulated so that all

energy transfers through the silver and polymer films. List the assumptions of your analysis.

$[k_{Au}=405\frac{W}{m}-K,k_{\text{p}\text{o}\text{l}\text{y}\text{m}\text{e}\text{r}}=0\mathrm{.}25\frac{W}{m}-K]$

List of Assumptions: