Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between the plates without touching any of them to reduce heat exchange between the plates. Assume that the emissivities of plates and radiation shield are equal. The ratio of the net heat exchange between the plates with and without the shield is

A hemispherical furnace of $$1$$ $$m$$ radius has the inner surface (emissivity, $$\varepsilon = 1$$) of its roof maintained at $$800K,$$ while its floor $$\left( {\varepsilon = 0.5} \right)$$ is kept at $$600K$$. Stefan-Boltzmannn constant is $$\,5.668 \times {10^{ - 8}}$$ $$W/{m^2}.{K^4}.$$ The net radiative heat transfer (in $$kW$$) from the roof to the floor is __________.

A solid sphere of radius$${r_1} = 20\,\,mm$$ is placed concentrically inside a hollow sphere of radius $${r_2} = 30\,\,mm$$ as shown in the figure.

The view factor $${F_{21}}$$ for radiation heat transfer is

Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of $$400$$ $$K$$ and $$300$$ $$K.$$ If the emissivities of the surfaces are $$0.8$$ and the Stefan-Boltzmann constant is $$5.67 \times {10^{ - 8}}$$ $$W/{m^2}{K^4},$$ the net radiation heat exchange rate in $$kW/{m^2}$$ between the two plates is