Consider the system depicted in Figure 8.3. Assume that the hot gas has properties similar to air, is at 1 bar pressure, has a temperature of 450 K, and flows with a velocity of U∞ = 25 m/s. The...

Consider the system depicted in Figure 8.3. Assume that the hot gas has properties similar to air, is at 1 bar pressure, has a temperature of 450 K, and flows with a velocity of U∞ = 25 m/s. The porous wall is 1 cm thick and is made of sintered stainless steel (AISI 302) with 50% porosity that has a measured permeability of b = 1.2 × 10⁻¹¹
m²
. The coolant is helium at a temperature of 300 K and pressure of 1.0025 bar. At a distance of 1.5 m from the leading edge, find the temperature and heat flux at the outer surface (i.e., the surface facing the hot gas) of the porous wall. Compare these results with the outer surface temperature and heat flux if transpiration was not applied. Assume steady state and assume that the convective heat transfer coefficient between the inner surface of the wall and helium is equal to 380 W/m²
⋅K. Neglect heat transfer by radiation. For the flow through the porous medium, assume that Darcy’s law applies, whereby,