QUESTION $2(35$ Marks$)$

An ostrich egg with a radius of $5$ cm will be modeled as a perfect sphere with a thermal conductivity of $0\mathrm{.}5\frac{W}{m}C,$ and a thermal diffusivity of $1\mathrm{.}5{10}^{-5}\frac{m^2}{s}.$ The egg is initially at a uniform temperature of $25C$ and dropped into boiling water at $95C.$ The convection heat transfer coefficient between the egg and water is $1000\frac{W}{m^2}.C.$

a$)$ Determine how long it will take for the centre of the egg to reach $60C.$

b$)$ What is the major assumption you used in solving this problem, is it satisfied?