problem 2 problem 13 7 atmospheric air with a temperature of 300 k flo

Question

PROBLEM 2
Problem 13.7. Atmospheric air, with a temperature of 300 K, flows through a 80 μm-thick porous
membrane. The membrane's porosity (total volume fraction of pores) is 25%. The accommodation
coefficients have been measured to be a = 0.79 and ath = 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.