Absorption in a Falling Thin Liquid Film at Low Reynolds Numbers

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Consider the absorption without chemical reaction of a gaseous species in a thin liquid film of a nonvolatile compound
flowing vertically at low Reynolds numbers.
Contributed by: Housam Binousand Brian G. Higgins (June 2013)
Open content licensed under CC BY-NC-SA
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Details
In the discrete Chebyshev–Gauss–Lobatto case, the interior points are given by . These points are the extrema of the Chebyshev polynomials of the first kind,
.
The Chebyshev derivative matrix at the quadrature points is an
matrix
given by
,
,
for
, and
for
,
, and
,
where for
and
.
The matrix is then used as follows:
and
, where
is a vector formed by evaluating
at
,
, and
and
are the approximations of
and
at the
.
References
[1] P. Moin, Fundamentals of Engineering Numerical Analysis, Cambridge, UK: Cambridge University Press, 2001.
[2] L. N. Trefethen, Spectral Methods in MATLAB, Philadelphia: SIAM, 2000.
[3] R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, 2nd ed., New York: John Wiley & Sons, 2002.
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