Consider steady$-$state conditions for one$-$dimensional conduction in a $1\mathrm{.}500mm$ wall, which is well insulated at $x=0.$ The wall experiences a uniform volumetric heat generation at a rate of $q=3000\frac{W}{m^3}.$ While at $x=L,$ the outer surface is cooled by a water stream with $T_{**}=4C$ and $h=1000\frac{W}{m^2}K.$ Neglecting the contact surface resistance, radiation and assuming constant thermal properties of the wall of $k=60\frac{W}{m}.K$ :

a$)$ Sketch the scheme and write the boundary conditions $(10$ pts$)$

b$)$ Find the outer surface temperature $T_x$ at $x=L.(\{$:$15pts)$

c$)$ Find the temperature distribution $T(x).(15pts)$

d$)$ Find the heat flux through the wall q$".(10pts$