root/trunk/matml/transport/problems/cdmold1/cdmold1.tex

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\begin{enumerate}
\item CD Injection Molding I: Navier-Stokes

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    \input{cd}
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  CDs are made cheaply in large quantity by injection molding polycarbonate
  into a nickel mold with precisely-machined bumps which form the ones and
  zeroes.  We would like to estimate the shear stress exerted by the
  polycarbonate on the nickel, in order to assess the lifetime of the mold
  (number of CDs it can make).

  The polymer flows from the center outward, and the viscosity is high enough
  and the mold thin enough ($\sim$1mm) that the ``entrance length'' is even
  smaller than the $\sim$1cm circle which is cut out of the center.

  \begin{enumerate}
  \item Using the accompanying handout {\em Solving Fluid Dynamics Problems},
    state the assumptions which you can make about flow through the thin
    mold.  You can ignore the outer region near the advancing front (the
    ``leading edge'' of the polymer), and also ignore the region very close to
    the center.
  \item Cancel the appropriate terms on the cylindrical Navier-Stokes
    equations, which you will detach from the handout and turn in.  You do {\em
      not} need to (and may not be able to) reduce it to a simple system which
    you can easily solve.
  \end{enumerate}
\end{enumerate}
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