It is observed that the temperature distribution, in steady$-$state, inside a one$-$dimensional wall with thermal conductivity of $50$ W$/$m$$K and a thickness of $50$ mm$,$ follows the form T$($C$)=$a$+$bx$2$T$(^\backslash$circ$\backslash$text$\{$C$\})=$ a $+$ bx$^2$T$($C$)=$a$+$bx$2,$ where a$=200$Ca $=200^\backslash$circ$\backslash$text$\{$C$\}$a$=200$C$,$ b$=2,000$C$/$m$2$b $=-2,000^\backslash$circ$\backslash$text$\{$C$\}/\backslash$text$\{$m$\}^2$b$=2,000$C$/$m$2,$ and xxx is in meters.

$($a$)$ What is the heat generation rate qqq in the wall?

$($b$)$ Determine the heat fluxes on both sides of the wall. How are these heat fluxes related to the heat generation rate?