Hydrogen gas is used in a process to manufacture asheet

Chapter 14, Problem 14.51

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Hydrogen gas is used in a process to manufacture asheet material of 6-mm thickness. At the end of theprocess, H2remains in solution in the material with auniform concentration of 320 kmol/m3. To remove H2from the material, both surfaces of the sheet areexposed to an airstream at 500 K and a total pressureof 3 atm. Due to contamination, the hydrogen partialpressure is 0.1 atm in the airstream, which provides a convection mass transfer coefficient of 1.5 m/h. Themass diffusivity and solubility of hydrogen (A) in the sheet material (B) are DAB?2.6?10?8m2/s andSAB?160 kmol/m3?atm, respectively.(a) If the sheet material is left exposed to the airstreamfor a long time, determine the final content ofhydrogen in the material (kg/m3).(b) Identify and evaluate the parameter that can beused to determine whether the transient mass dif-fusion process in the sheet can be assumed to becharacterized by a uniform concentration at anytime during the process. Hint: This situation isanalogous to that used to determine the validity ofthe lumped-capacitance method for a transientheat transfer analysis.(c) Determine the time required to reduce the hydro-gen mass density at the center of the sheet totwice the limiting value calculated in part (a)