$1.$ Which approach would you use to answer the following question $($Lumped Capacitance, specific geometry, semi$-$infinite solid approximation, or computational approach$)?$ Be sure to justify your answer. If there is insufficient information to select an approach, say what additional information would be needed. You do not need to answer the questions, just say which approach you would use, but you do need to show your reasoning! $($Note: you should be able to do this question without using a calculator$).$

A plane wall is cooled symmetrically from an initial temperature of $\backslash (500^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ by jets of $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ water sprayed on both sides. The convection heat transfer coefficient for the problem is $\backslash ($ h$=3$ W $/\backslash$mathrm$\{$m$\}^\{2\}\backslash$mathrm$\{$~K$\}\backslash ).$ The wall has thickness $1$ m $,$ density $\backslash (\backslash$rho$=1\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash ),$ specific heat $\backslash (\backslash$mathrm$\{$c$\}=2\backslash$mathrm$\{$~J$\}/\backslash$mathrm$\{$kgK$\}\backslash ),$ and thermal conductivity $\backslash (\backslash$mathrm$\{$k$\}=16\backslash$mathrm$\{$~W$\}/\backslash$mathrm$\{$mK$\}\backslash ).$ What is the surface temperature of the wall after $10$ s $?$