Atmospheric air, with a temperature of 300 K, flows through an 80-μm-thick porous membrane. The membrane’s porosity (total volume fraction of pores) is 25%. The accommodation coefficients have been...

Atmospheric air, with a temperature of 300 K, flows through an 80-μm-thick porous membrane. The membrane’s porosity (total volume fraction of pores) is 25%. The accommodation coefficients have been measured to be α = 0.79 and α_th
= 0.24. The superficial velocity of air through the membrane (velocity calculated based on the total membrane area) is 3.0 m/s. Assume that the pores can be idealized as smooth-walled circular flow passages 5 μm in diameter.

(a) Calculate the total pressure drop across the membrane.

(b) Neglecting heat transfer from the front and back surfaces of the membrane, calculate the thermal load that can be removed by air, in watts per square meter of the membrane, assuming that the air mean temperature reaches 301 K. Estimate the membrane temperature, assuming that the membrane remains isothermal.