Consider a square copper plate whose sides are $0\mathrm{.}45$ m long and thickness of $2\mathrm{.}5$ cm$,$ initially at $35$C$.$ The plate is exposed to liquid nitrogen undergoing phase change at $-196$C$,$ with a convective heat transfer coefficient of $275$ W$/$m$-$k$.$ Determine the amount of time that the plate can be in contact with the cold fluid before it reaches the minimum allowable temperature of $-40$C$.$ The thermal properties of copper are given: cp $=0\mathrm{.}381$ J$/$kg$-$K$,$ k $=404$ W$/$mK$,$ p $=8941$ kg$/$m$^3.$