Problem $1(3$ points$)$: A plane wall of thickness $L=0\mathrm{.}5m$ has a thermal conductivity of $k_w=8\frac{W}{m}-K.$ The outer surface of the wall, at location $x=L,$ is at a temperature $T_o=45C,$ and the inner surface temperature $T_i$ is unknown. It is known that the outer surface of the wall exchanges heat with surrounding air by convection heat transfer. The convection heat transfer coefficient is $h=15\frac{W}{m^2}-K.$ Temperature of air surrounding the outer surface of the wall is $T_{}=368K.$ Assuming steadystate $1-$D heat transfer with no energy generation,

Will conductive flux through the wall remain constant? No need to prove anything explicitly. Just state a simple reason as to why$/$why not?

Determine the temperature at the inner surface of the wall, at location $x=0m.$

Sketch the temperature profile through the wall. State the direction of heat transfer through the wall.