In a furnace, the inner and outer sides of the brick wall $(k_1=2.5 \: \text{W/m.k})$ are maintained at $1100 ^\circ C$ and $700 ^\circ C$, respectively as shown in figure.
The brick wall is covered by an insulating material of thermal conductivity $k_2$. The thickness of the insulation is $1/4$th of the thickness of the brick wall. The outer surface of the insulation is at $200^\circ C$. The heat flux through the composite walls is $2500 \: W/m^2$.
The value of $k_2$ is _______ $\text{W/m.K}$ (round off to one decimal place)