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

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

A company uses 3000 units of a part annually. The units are priced as given in the table below. It costs Rs. 150 to place an order. Carrying costs are 40 percent of the purchase price per unit on an annual basis. The minimum total annual cost is Rs. ____________ (rounded off to 1 decimal place).

$$ \begin{array}{|c|c|} \hline \text { Order quantity } & \text { Unit price(Rs.) } \\ \hline \text { 1 to 499 } & 9.0 \\ \hline \text { 500 to 999 } & 8.5 \\ \hline \text { 1000 or more } & 8.0 \\ \hline \end{array} $$