Figure $1$ shows a hot $\backslash (50-\backslash$mathrm$\{$cm$\}\backslash )$ thick brass plate is having its upper surface cooled by an impinging jet of air at temperature of $\backslash (15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ that create convection heat transfer coefficient of $\backslash (220\backslash$frac$\{\backslash$mathrm$\{$~W$\}\}\{\backslash$mathrm$\{$~m$\}^\{2\}\backslash$mathrm$\{$k$\}\}\backslash ).$ The brass plate has a uniform initial temperature of $\backslash (650^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ),$ and the bottom surface of the plate is insulated.

$($a$)$ Determine the temperature at the plate surface and at the center plane of the brass plate after $60$s of cooling

$($b$)$ Determine the heat flux at the plate surface and at the center plane of the brass plate after $60$s of cooling

$($c$)$ Provide three engineering assumptions and engineering model for solving $($ a and b $)$