Consider a velocity field $\vec{V}=3 z \hat{i}+0 \hat{j}+C x \hat{k}$, where $C$ is a constant. if the flow is irrotational, the value of C is ________ (rounded off to 1 decimal place).

Let a spherical block of ice at $-7^{\circ} \mathrm{C}$ be exposed to atmospheric air at $30^{\circ} \mathrm{C}$ with the gravitational direction as shown in the figure below. What will be the overall direction of air flow in this situation?

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, $\sigma=5.67 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}$.