Question $1)[35$ Pts$]$

Consider a large plane wall $($See the Figure$)$ of thickness $L=0\mathrm{.}3m,$ a thermal

conductivity of $1\mathrm{.}2\frac{W}{m}.K$ The width and the height of the plane are $3$ m and $5$ m

respectively. The two sides of the wall are maintained at constant temperatures of

$T_1=130C$ and $T_2=40C$ respectively. Heat transfer is in the x $-$direction only.

A$)$ Write the differential equation describing the heat transfer. $[6$ Pts$]$

B$)$ Mention the boundary conditions. $[4$ Pts$]$

C$)$ Derivethe algebraic expression that estimates temperature T$.[15$ Pts$]$

D$)$ Determine the temperature at the middle of the wall $($at $x=0\mathrm{.}15m).[5$ Pts$]$

E$)$ In case the two sides were not maintained at constant temperatures, what would be

the differential equation describing this heat transfer? $[5$ Pts$]$