Steady one-dimensional heat conduction takes place across the faces $$1$$ and $$3$$ of a composite slab consisting of slabs $$A$$ and $$B$$ in perfect contact as shown in the figure, where $${k_A},\,\,{k_B}$$ denote the respective thermal conductivities. Using the data as given in the figure, the interface temperature $${T_2}$$ $$\left( {in\,{\,^ \circ }C\left. \, \right)} \right.$$ is ______________.

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 _____________.

For a heat exchanger, $$\Delta {T_{\max }}$$ is the maximum temperature difference and $$\Delta {T_{\min }}$$ is the minimum temperature difference between the two fluids. $$LMTD$$ is the log mean temperature difference. $${C_{\min }}$$ and $${C_{\max }}$$ are the minimum and the maximum heat capacity rates. The maximum possible heat transfer $$\left( {{Q_{\max }}} \right)$$ between the two fluids is

In $$PERT$$ chart, the activity time distribution is