In a furnace, the inner and outer sides of the brick wall (k1 = 2.5 W/mK) are maintained at 1100°C and 700°C respectively as shown in figure.

The brick wall is covered by an insulating material of thermal conductivity k2. The thickness of the insulation is 1/4th of the thickness of the brick wall. The outer surface of the insulation is at 200°C. The heat flux through the composite walls is 2500 W/m2. The value of k2 is ________ W/mK (round off to 2 decimal places).

The correct answer is 0.5.

Step-by-step Explanation:

Based on the provided schematic diagram of the furnace wall, we can observe the following labels, data points, and configuration:
1. A composite wall consisting of a Brick wall of thickness $L_1$ and thermal conductivity $k_1=2.5\text{W/mK}$ adjacent to an Insulation layer of thickness $L_2$ and thermal conductivity $k_2$.
2. The boundary temperatures are maintained at $1100\text{°C}$ on the inner side, $700\text{°C}$ at the brick-insulation interface, and $200\text{°C}$ on the outer side of the insulation.
3. The thickness relationship is given by the equation:

$L_2=\frac{L_1}{4}$

4. Under steady-state conditions, a uniform heat flux passes through both walls:

$q=2500{\text{W/m}}^2$

Applying Fourier's Law of Heat Conduction:
Under steady-state conditions, the rate of heat transfer per unit area (heat flux, $q$) is constant through both sections of the composite wall. Therefore, we can equate the heat flux through the brick wall to the heat flux through the insulation material:

$q=k_1\frac{\Delta T_1}{L_1}=k_2\frac{\Delta T_{\mathrm{2<!--\; </msub-->}}}{L_2}$

Where:
- For the brick wall:

- For the insulating layer: