A furnace wall slab

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A furnace wall slab is constructed with fire clay of thickness 90 mm (L1) inside and red brick of thickness 450 mm (L2) outside. The temperatures inside and outside the furnace wall are 1100°C (T1) and 30°C (T3), respectively. The thermal conductivity of the red brick (K2) is 0.8W/m K and that of the fire clay (K1), is 0.3(1 + 0.001T) W/m K where T is the temperature of the clay in degrees Celsius. Assuming unit surface area, find the conductive heat loss through the furnace wall and the temperature at the interface of the fire clay and red brick.

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