During a welding operation, thermal power of 2500 W is incident normally on a metallic surface. As shown in the figure below (figure is NOT to scale), the heated area is circular. Out of the incident power, $85 \%$ of the power is absorbed within a circle of radius 5 mm while $65 \%$ is absorbed within an inner concentric circle of radius 3 mm . The power density in the shaded area is __________ $\mathrm{Wmm}^{-2}$ (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, $\sigma=5.67 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}$.

Water enters a tube of diameter, $D=60 \mathrm{~mm}$ with mass flow rate of $0.01 \mathrm{~kg} \mathrm{~s}^{-1}$ as shown in the figure below. The inlet mean temperature is $T_{m, i}=293 \mathrm{~K}$ and the uniform heat flux at the surface of the tube is $2000 \mathrm{Wm}^{-2}$. For the exit mean temperature of $T_{m, o}=$ 353 K , the length of the tube, $L$ is ___________ m (rounded off to 1 decimal place). Use the specific heat of water as $4181 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$.

Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, are

$$ \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \text { Period } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \text { Actual demand } & 425 & 415 & 420 & 430 & 427 & 418 & 422 & 416 & 426 & 421 \\ \hline \text { Forecast } & 427 & 422 & 416 & 422 & 423 & 420 & 419 & 418 & 430 & 415 \\ \hline \end{array} $$