A stainless steel part with temperature of $420\backslash$deg C is taken out of an oven to cool down in air. Ambient air temperature is $20\backslash$deg C and the convection heat transfer coefficient is $=20$ W$.$m$-2$K$-1($radiation negligible$).$ The part has a surface area of A$=2$ cm$2$ and a volume of V$=0\mathrm{.}3$ cm$3.$ It can be approximated as a cylinder if needed. How long does it take for the temperature at the center to reach $120\backslash$deg C$?$ Specify and justify all assumptions.Properties of stainless steel: $k=12W*m^{-1}{K}^{-1},=8000kg*m^{-3},c_p=0\mathrm{.}5kJ*k{g}^{-1}{K}^{-1}$

Properties of air: $,k=0\mathrm{.}025W*m^{-1}{K}^{-1},=1\mathrm{.}2kg*m^{-3},c_p=1\mathrm{.}0kJ*k{g}^{-1}{K}^{-1}$