A furnace wall is made up of three layers, the inner one of firebrick, the middle one of insulating brick and the outer one of red brick, of thermal conductivities 1.21, 0.13 and 0.85 W m-1 K-1 respectively, and thicknesses 200 mm, 70 mm and 95 mm, respectively. The inner wall is at 900C, and the heat flux is 1000 W m-2 i) Why, at steady state, is the heat flux across each layer the same, even though the thicknesses and thermal conductivities are different? ii) Assuming close bonding between each layer at their interfaces, calculate the temperature at each interface and at the outer wall. iii) Layer 1 is the thickest one among three layers, can we say that layer 1 has controlling thermal resistance? Which layer is the controlling thermal resistance? Support your answer with a numerical argument. iv) Draw a diagram showing the temperature profile across the wall, with particular emphasis on the slopes of the lines