$(15$ points$)$ A cubic block $(0\mathrm{.}6m0\mathrm{.}6m0\mathrm{.}6m)$ of rubber is to be cooled down after heating it to a uniform temperature of $420$ K $,$ how long $($in hours$)$ will it take for the center of block to reach $320$ K if cool air is blown over all of the surfaces at $277$ K with an effective convective heat transfer coefficient $230\frac{W}{m^2}*K.$ Properties of rubber that may be used are following: $k_{\text{r}\text{u}\text{b}\text{b}\text{e}\text{r}}=0\mathrm{.}151\frac{W}{m}*K,C_p=200\frac{J}{k}g*K,=1201k\frac{g}{m^3},={6\mathrm{.}1910}^{-8}\frac{m^2}{sec}.$

$($hint: Check Bi number to guide approach$)$