Question: Let air at 540°C and 1 atm pressure flow at a velocity of 6 mls normal to a 2.5 cm diameter cylinder. Let the cylinder be of a thin-walled porous material so that air can be pumped inside the cylinder and out through the pores in order to cool the walls. Let the cooling air be at 40°C where it actually enters the porous material. The objective of the problem is to calculate the cylinder surface temperature in the region of the stagnation point for various cooling-air flow rates, expressed as the mass rate of cooling air per square meter of cylinder surface. The problem is to be worked first for no radiation and then assuming that the cylinder surface is a black body radiating to a large surrounding (say a large duct) at 540°C. The same cooling air could be used to cool the surface internally by convection without passing through the surface out into the main stream. Assuming that the cooling air is again available at 40°C and is ducted away from the surface at surface temperature, calculate the surface temperature as a function of cooling-air rate per square meter of cylinder surface area for this case and compare with the results above.