GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

In a furnace, the inner and outer sides of the brick wall $\left({\mathit{k}}_1=2.5\mathit{W}/\mathit{m}\cdot \mathit{K}\right)$ are maintained at ${1100}^{\circ }\mathit{C}$ and ${700}^{\circ }\mathit{C}$, respectively as shown in figure. The brick wall is covered by an insulating material of thermal conductivity ${\mathit{k}}_2$. The thickness of the insulation is of the thickness of the brick wall. The outer surface of the insulation is at ${200}^{\circ }\mathit{C}$. The heat flux through the composite walls is $2500\mathit{W}/{\mathit{m}}^2$. The value of ${\mathit{k}}_2$ is ___________W/m.K (round off to one decimal place).