$3.(25$ points$)$ A solid plate $($edge effect can be ignored$)$ with thickness of $\backslash ($ b $\backslash )$ is initially at temperature $\backslash ($ T$\_\{0\}\backslash ).$ At time $\backslash ($ t$=0\backslash ),$ it is suddenly immerged in a liquid at temperature $\backslash ($ T$\_\{1\}\backslash )$ as shown in following figure. Assume the liquid quantity is large enough that the temperature won't change. The thermal conductivity, heat capacity $($mass based$),$ density of the solid material is $\backslash (\backslash$mathrm$\{$k$\},\backslash$mathrm$\{$C$\}\_\{$p$\}\backslash )$ and $\backslash (\backslash$rho $\backslash ),$ respectively. The Newton's law of cooling can be applied for heat transfer between the liquid and solid. The heat transfer coefficient is h $.$ Write down the governing equation and boundary and initial conditions for calculating T as a function of location $($y$)$ and t$.$