Exercise $2$:

Fig.l: Bricks wall insulated using two insulation layers

We consider a wall made of bricks insulated using two insulation layers. Only one dimensional conduction is considered $($in the x $-$axis direction$).$ The temperature of ambient air outside the wall is denoted $T_0.$ The wall exchanges heat with the outside by convection and the heat convection coefficient is denoted $h_o($at $x=0).$ The boundary condition at $x=e_{\text{t}\text{o}\text{t}}$ is an imposed fixed temperature $T_i.$

Give the expression of the global thermal resistance in $\frac{K}{W}$ and explain each term. Calculate its value.

Give the expression of the global thermal resistance per unit of area in $K.\frac{m^2}{W}$ and calculate its value.

Calculate the heat rate and the heat flux through the insulated wall.

Calculate the temperature $T_1$ at the surface of the bricks wall $($see fig. $1).$

If only the insulation layer $1$ is used to insulate the wall, what would be the thickness of this layer to obtain the same global thermal resistance as in question $1?$

$\backslash$table$[[$Data$],[\backslash$table$[[$Wall$\text{'}$s area $(A),20m^2$