A novel process has been proposed to create a com-posite

Chapter 14, Problem 14.33

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A novel process has been proposed to create a com-posite palladium tube for use as a hydrogen separationmembrane in order to produce high-purity hydrogen.To fabricate the composite palladium tube, a gas con-taining palladium (species A) flows through a porous-walled tube, and the palladium deposits into the poresof the tube wall. The gas mass flow rate is andthe inlet mass concentration of palladium is ?A,m,i. Themass transfer coefficient for transfer of palladiumbetween the gas and the surface is hm, and the deposi-tion rate is proportional to the mass concentration ofpalladium at the tube surface, that is, ?n?A,s?k1?A,s.The palladium is a dilute species, so the total massflow rate is approximately constant down the length ofthe tube.(a) Building upon the convection mass transfer analy-sis presented in Section 8.9, derive an expressionfor the variation of the mean species density of pal-ladium with distance from the tube entrance, anddetermine an expression for the local depositionrate (kg/m2?s) for a tube of diameter D. Neglectany leakage of gas through the porous tube walls.(b) If the tube is too long, the variation in depositthickness will be unacceptably large. What is theratio of the deposition rates at x?Land x?0?