root/trunk/matml/transport/problems/hepyrex/hepyrex.tex

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\begin{enumerate}
\item Helium diffusion through a pyrex tube
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  The diffusivity of helium in pyrex glass is vastly higher than that of any
  other gas.  (Indeed, it is around 25 times larger than that of hydrogen, its
  closest competitor.)  For this reason, it has been suggested that pyrex
  tubing be used as a filter to extract helium from natural gas.  Here we will
  calculate the rate of helium production by diffusion through small pyrex
  tubes.

  \begin{enumerate}
  \item Write the differential equation for steady-state 1-D diffusion in the
    radial direction in cylindrical coordinates, and the general form of the
    solution.

  \item Write the solution for constant concentrations of helium on the inside
    and outside of the tube, {\em i.e.} $C_{\rm He, in}$ at the inner radius
    $R_{\rm in}$, and $C_{\rm He, out}$ at the outer radius $R_{\rm out}$.

  \item At 500$^\circ$ C, $D_{\rm He-pyrex}=2\times 10^{-8}\ \frac{\rm
      cm^2}{\rm s}$.  Assuming the helium concentration in pyrex in equilibrium
    with a steady stream of natural gas/helium mixture $C_{\rm He, in}$ is
    10$^{-5}$ $\rm\frac{g}{cm^3}$, and the helium concentration on the outside
    of the tubes $C_{\rm He, out}$ is 0, calculate the rate of helium
    extraction in a small tube array apparatus with 0.5 mm thick tubes with
    outer diameter of 2mm, and a total tube length of 10 meters (say, 100 tubes
    each 10 cm in length).  Give the rate in cubic meters of helium at STP per
    hour.
  \end{enumerate}
\end{enumerate}
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