Problem $2.$

A one$-$dimensional plane wall of thickness $2L=80mm$ experiences uniform thermal energy

generation of $q^{}=1000\frac{W}{m^3}$ and is convectively cooled at $x=+-40mm$ by an ambient fluid

characterized by $T_{}=30C.$ If the steady$-$state temperature distribution within the wall is

$T(x)=a(L^2-x^2)+b$ where $a=15\frac{C}{m^2}$ and $b=40C,$ find:

$($a$)$ the thermal conductivity $(k)$ of the wall, $(3$pt$)$

$($b$)$ the convection heat transfer coefficient $(h).(2$pt$)$