Two black surfaces, $$AB$$ and $$BC,$$ of lengths $$5m$$ and $$6m,$$ respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view factor $${F_{12}} = 0.5,\,\,{T_1} = 800\,\,K,\,\,{T_2} = 600\,\,K,$$ $${T_{surrounding}} = 300\,\,K$$ and Stefan Boltzmann constant, $$\sigma = 5.67 \times {10^{ - 8}}\,\,W/\left( {{m^2}{K^4}} \right),$$ the heat transfer rate from Surface $$2$$ to the surrounding environment is ____________ $$kW.$$

Two large parallel plates having a gap of $$10$$ $$mm$$ in between them are maintained at temperatures $${T_1} = 1000\,\,K$$ and $${T_2} = 400\,\,K$$
Given emissivity values, $${\varepsilon _1} = 0.5,\,\,{\varepsilon _2} = 0.25$$ and Stefan-Boltzmann constant $$\sigma = 5.67 \times {10^{ - 8}}\,$$ $$\,W/{m^2}$$-$$K,$$ the heat transfer between the plates (in $$kW/{m^2}$$) is _____________.

An infinitely long furnace of $$0.5m \times 0.4m$$ cross-section is shown in the figure below. Consider all surfaces of the furnace to be black. The top and bottom walls are maintained at temperature $${T_1} = {T_3} = {927^ \circ }C,$$
while the side walls are at temperature $${T_2} = {T_4} = {527^ \circ }C.$$
The view factor, $${F_{1 - 2}}$$ is $$0.26.$$ The net radiation heat loss or gain on side $$1$$ is_________ $$W/m.$$ Stefan-Boltzman constant $$ = \,5.67 \times {10^{ - 8}}$$ $$W/{m^2}$$-$${K^4}$$

A solid sphere $$1$$ of radius $$'r'$$ is placed inside a hollow, closed hemispherical surface $$2$$ of radius $$'4r'.$$ The shape factor $${F_{2 - 1}}$$ is ...