Two rectangular surfaces both having $1 \mathrm{~m}^2$ area are placed perpendicular to each other with a common edge. One surface is hot, having a temperature of 1000 K and emissivity of 0.4 , while the other is insulated and in radiant balance with a large surrounding room at 300 K . If the fraction of radiation leaving the hot surface which reaches the cold surface is 0.2 , then the equivalent overall resistance for the radiation heat loss from the hot surface is $\_\_\_\_$ $\mathrm{m}^{-2}$ (rounded off to 2 decimal places).

Consider a cylindrical furnace of 5 m diameter and 5 m length with bottom, top and curved surfaces maintained at uniform temperatures of $800 \mathrm{~K}, 1500 \mathrm{~K}$ and 500 K , respectively. The view factor between the bottom and top surfaces, $F_{12}$ is 0.2 . The magnitude of net radiation heat transfer rate between the bottom surface and the curved surface is _________ kW (rounded off to 1 decimal place).

All surfaces of the furnace can be assumed as black.

The Stefan-Boltzmann constant, $\sigma=5.67 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}$.

Consider a hemispherical furnace of diameter $ D = 6 \text{ m} $ with a flat base. The dome of the furnace has an emissivity of 0.7 and the flat base is a blackbody. The base and the dome are maintained at uniform temperature of 300 K and 1200 K, respectively. Under steady state conditions, the rate of radiation heat transfer from the dome to the base is _______ kW (rounded off to the nearest integer).

Use Stefan-Boltzmann constant = $5.67 \times 10^{-8} \text{ W/(m}^2 \text{ K}^4 \text{)}$