A $5\mathrm{.}5-$cm$-$diameter spherical shaped egg is initially at a uniform temperature of $8C$ and is dropped into boiling water at $97C.$ Taking the convection heat transfer coefficient to be h $=1400\frac{W}{m^2}*C,$ determine how long it will take for the center of the egg to reach $70C.$ and $=0\mathrm{.}14{10}^{-6}\frac{m^2}{s})$